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<span>History</span> </div> </a> <button aria-controls="toc-History-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle History subsection</span> </button> <ul id="toc-History-sublist" class="vector-toc-list"> <li id="toc-Gauge_supersymmetry" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Gauge_supersymmetry"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Gauge supersymmetry</span> </div> </a> <ul id="toc-Gauge_supersymmetry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Supergravity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Supergravity"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Supergravity</span> </div> </a> <ul id="toc-Supergravity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-mSUGRA" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#mSUGRA"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>mSUGRA</span> </div> </a> <ul id="toc-mSUGRA-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-11D:_the_maximal_SUGRA" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#11D:_the_maximal_SUGRA"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>11D: the maximal SUGRA</span> </div> </a> <ul id="toc-11D:_the_maximal_SUGRA-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-The_end_of_the_SUGRA_era" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#The_end_of_the_SUGRA_era"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>The end of the SUGRA era</span> </div> </a> <ul id="toc-The_end_of_the_SUGRA_era-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-The_second_superstring_revolution" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#The_second_superstring_revolution"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>The second superstring revolution</span> </div> </a> <ul id="toc-The_second_superstring_revolution-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Relation_to_superstrings" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Relation_to_superstrings"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Relation to superstrings</span> </div> </a> <ul id="toc-Relation_to_superstrings-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-4D_N_=_1_SUGRA" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#4D_N_=_1_SUGRA"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>4D <i>N</i> = 1 SUGRA</span> </div> </a> <ul id="toc-4D_N_=_1_SUGRA-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-N_=_8_supergravity_in_4_dimensions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#N_=_8_supergravity_in_4_dimensions"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span><i>N</i> = 8 supergravity in 4 dimensions</span> </div> </a> <ul id="toc-N_=_8_supergravity_in_4_dimensions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Higher-dimensional_SUGRA" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Higher-dimensional_SUGRA"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Higher-dimensional SUGRA</span> </div> </a> <ul id="toc-Higher-dimensional_SUGRA-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Bibliography</span> </div> </a> <button aria-controls="toc-Bibliography-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Bibliography subsection</span> </button> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> <li id="toc-Historical" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Historical"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.1</span> <span>Historical</span> </div> </a> <ul id="toc-Historical-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-General" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#General"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.2</span> <span>General</span> </div> </a> <ul id="toc-General-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Supergravity</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" 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Available in 33 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-33" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">33 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AC%D8%A7%D8%B0%D8%A8%D9%8A%D8%A9_%D9%81%D8%A7%D8%A6%D9%82%D8%A9" title="جاذبية فائقة – Arabic" lang="ar" hreflang="ar" data-title="جاذبية فائقة" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D1%83%D0%BF%D0%B5%D1%80%D0%B3%D1%80%D0%B0%D0%B2%D1%96%D1%82%D0%B0%D1%86%D1%8B%D1%8F" title="Супергравітацыя – Belarusian" lang="be" hreflang="be" data-title="Супергравітацыя" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Supergravitace" title="Supergravitace – Czech" lang="cs" hreflang="cs" data-title="Supergravitace" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Supergravitation" title="Supergravitation – German" lang="de" hreflang="de" data-title="Supergravitation" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Supergravitatsioon" title="Supergravitatsioon – Estonian" lang="et" hreflang="et" data-title="Supergravitatsioon" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A5%CF%80%CE%B5%CF%81%CE%B2%CE%B1%CF%81%CF%8D%CF%84%CE%B7%CF%84%CE%B1" title="Υπερβαρύτητα – Greek" lang="el" hreflang="el" data-title="Υπερβαρύτητα" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Supergravedad" title="Supergravedad – Spanish" lang="es" hreflang="es" data-title="Supergravedad" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D8%A8%D8%B1%DA%AF%D8%B1%D8%A7%D9%86%D8%B4" title="ابرگرانش – Persian" lang="fa" hreflang="fa" data-title="ابرگرانش" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Supergravit%C3%A9" title="Supergravité – French" lang="fr" hreflang="fr" data-title="Supergravité" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Forimtharraingt" title="Forimtharraingt – Irish" lang="ga" hreflang="ga" data-title="Forimtharraingt" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%B4%88%EC%A4%91%EB%A0%A5" title="초중력 – Korean" lang="ko" hreflang="ko" data-title="초중력" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Supergravitasi" title="Supergravitasi – Indonesian" lang="id" hreflang="id" data-title="Supergravitasi" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Supergravit%C3%A0" title="Supergravità – Italian" lang="it" hreflang="it" data-title="Supergravità" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A1%D1%83%D0%BF%D0%B5%D1%80%D0%B3%D1%80%D0%B0%D0%B2%D0%B8%D1%82%D0%B0%D1%86%D0%B8%D1%8F" title="Супергравитация – Kazakh" lang="kk" hreflang="kk" data-title="Супергравитация" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A1%D1%83%D0%BF%D0%B5%D1%80%D0%B3%D1%80%D0%B0%D0%B2%D0%B8%D1%82%D0%B0%D1%86%D0%B8%D1%8F" title="Супергравитация – Kyrgyz" lang="ky" hreflang="ky" data-title="Супергравитация" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Supergravitacija" title="Supergravitacija – Lithuanian" lang="lt" hreflang="lt" data-title="Supergravitacija" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Szupergravit%C3%A1ci%C3%B3" title="Szupergravitáció – Hungarian" lang="hu" hreflang="hu" data-title="Szupergravitáció" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Supergravitatie" title="Supergravitatie – Dutch" lang="nl" hreflang="nl" data-title="Supergravitatie" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%B6%85%E9%87%8D%E5%8A%9B%E7%90%86%E8%AB%96" title="超重力理論 – Japanese" lang="ja" hreflang="ja" data-title="超重力理論" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Supergravitasjon" title="Supergravitasjon – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Supergravitasjon" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B8%E0%A9%81%E0%A8%AA%E0%A8%B0-%E0%A8%97%E0%A8%B0%E0%A9%88%E0%A8%B5%E0%A8%BF%E0%A8%9F%E0%A9%80" title="ਸੁਪਰ-ਗਰੈਵਿਟੀ – Punjabi" lang="pa" hreflang="pa" data-title="ਸੁਪਰ-ਗਰੈਵਿਟੀ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Supergrawitacja" title="Supergrawitacja – Polish" lang="pl" hreflang="pl" data-title="Supergrawitacja" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Supergravita%C3%A7%C3%A3o" title="Supergravitação – Portuguese" lang="pt" hreflang="pt" data-title="Supergravitação" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Supergravita%C8%9Bie" title="Supergravitație – Romanian" lang="ro" hreflang="ro" data-title="Supergravitație" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D1%83%D0%BF%D0%B5%D1%80%D0%B3%D1%80%D0%B0%D0%B2%D0%B8%D1%82%D0%B0%D1%86%D0%B8%D1%8F" title="Супергравитация – Russian" lang="ru" hreflang="ru" data-title="Супергравитация" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Supergravitaatio" title="Supergravitaatio – Finnish" lang="fi" hreflang="fi" data-title="Supergravitaatio" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Supergravitation" title="Supergravitation – Swedish" lang="sv" hreflang="sv" data-title="Supergravitation" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/Supergravitatsi%C3%A4" title="Supergravitatsiä – Tatar" lang="tt" hreflang="tt" data-title="Supergravitatsiä" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/S%C3%BCper_k%C3%BCtle%C3%A7ekimi" title="Süper kütleçekimi – Turkish" lang="tr" hreflang="tr" data-title="Süper kütleçekimi" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a 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class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Modern theory of gravitation that combines supersymmetry and general relativity</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output 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.sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><th class="sidebar-title"><a href="/wiki/Physics_beyond_the_Standard_Model" title="Physics beyond the Standard Model">Beyond the Standard Model</a></th></tr><tr><td class="sidebar-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:CMS_Higgs-event.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/CMS_Higgs-event.jpg/220px-CMS_Higgs-event.jpg" decoding="async" width="220" height="203" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/CMS_Higgs-event.jpg/330px-CMS_Higgs-event.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/CMS_Higgs-event.jpg/440px-CMS_Higgs-event.jpg 2x" data-file-width="1104" data-file-height="1018" /></a></span><div class="sidebar-caption">Simulated <a href="/wiki/Large_Hadron_Collider" title="Large Hadron Collider">Large Hadron Collider</a> <a href="/wiki/Compact_Muon_Solenoid" title="Compact Muon Solenoid">CMS</a> particle detector data depicting a <a href="/wiki/Higgs_boson" title="Higgs boson">Higgs boson</a> produced by colliding protons decaying into hadron jets and electrons</div></td></tr><tr><th class="sidebar-heading"> <a href="/wiki/Standard_Model" title="Standard Model">Standard Model</a></th></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed hlist"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;color: var(--color-base)">Evidence</div><div class="sidebar-list-content mw-collapsible-content plainlist"> <ul><li><a href="/wiki/Hierarchy_problem" title="Hierarchy problem">Hierarchy problem</a></li> <li><a href="/wiki/Dark_matter" title="Dark matter">Dark matter</a></li> <li><a href="/wiki/Dark_energy" title="Dark energy">Dark energy</a></li> <li><a href="/wiki/Quintessence_(physics)" title="Quintessence (physics)">Quintessence</a></li> <li><a href="/wiki/Phantom_energy" title="Phantom energy">Phantom energy</a></li> <li><a href="/wiki/Dark_radiation" title="Dark radiation">Dark radiation</a></li> <li><a href="/wiki/Dark_photon" title="Dark photon">Dark photon</a></li> <li><a href="/wiki/Cosmological_constant_problem" title="Cosmological constant problem">Cosmological constant problem</a></li> <li><a href="/wiki/CP_violation" title="CP violation">Strong CP problem</a></li> <li><a href="/wiki/Neutrino_oscillation" title="Neutrino oscillation">Neutrino oscillation</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed hlist"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;color: var(--color-base)">Theories</div><div class="sidebar-list-content mw-collapsible-content plainlist"> <ul><li><a href="/wiki/Brans%E2%80%93Dicke_theory" title="Brans–Dicke theory">Brans–Dicke theory</a></li> <li><a href="/wiki/Cosmic_censorship_hypothesis" title="Cosmic censorship hypothesis">Cosmic censorship hypothesis</a></li> <li><a href="/wiki/Fifth_force" title="Fifth force">Fifth force</a></li> <li><a href="/wiki/F-theory" title="F-theory">F-theory</a></li> <li><a href="/wiki/Theory_of_everything" title="Theory of everything">Theory of everything</a></li> <li><a href="/wiki/Unified_field_theory" title="Unified field theory">Unified field theory</a></li> <li><a href="/wiki/Grand_Unified_Theory" title="Grand Unified Theory">Grand Unified Theory</a></li> <li><a href="/wiki/Technicolor_(physics)" title="Technicolor (physics)">Technicolor</a></li> <li><a href="/wiki/Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein theory</a></li> <li><a href="/wiki/6D_(2,0)_superconformal_field_theory" title="6D (2,0) superconformal field theory">6D (2,0) superconformal field theory</a></li> <li><a href="/wiki/Noncommutative_quantum_field_theory" title="Noncommutative quantum field theory">Noncommutative quantum field theory</a></li> <li><a href="/wiki/Quantum_cosmology" title="Quantum cosmology">Quantum cosmology</a></li> <li><a href="/wiki/Brane_cosmology" title="Brane cosmology">Brane cosmology</a></li> <li><a href="/wiki/String_theory" title="String theory">String theory</a></li> <li><a href="/wiki/Superstring_theory" title="Superstring theory">Superstring theory</a></li> <li><a href="/wiki/M-theory" title="M-theory">M-theory</a></li> <li><a href="/wiki/Mathematical_universe_hypothesis" title="Mathematical universe hypothesis">Mathematical universe hypothesis</a></li> <li><a href="/wiki/Mirror_matter" title="Mirror matter">Mirror matter</a></li> <li><a href="/wiki/Randall%E2%80%93Sundrum_model" title="Randall–Sundrum model">Randall–Sundrum model</a></li> <li><a href="/wiki/N_%3D_4_supersymmetric_Yang%E2%80%93Mills_theory" title="N = 4 supersymmetric Yang–Mills theory">N = 4 supersymmetric Yang–Mills theory</a></li> <li><a href="/wiki/Twistor_string_theory" title="Twistor string theory">Twistor string theory</a></li> <li><a href="/wiki/Dark_fluid" title="Dark fluid">Dark fluid</a></li> <li><a href="/wiki/Doubly_special_relativity" title="Doubly special relativity">Doubly special relativity</a></li> <li><a href="/wiki/De_Sitter_invariant_special_relativity" title="De Sitter invariant special relativity">de Sitter invariant special relativity</a></li> <li><a href="/wiki/Causal_fermion_system" class="mw-redirect" title="Causal fermion system">Causal fermion systems</a></li> <li><a href="/wiki/Black_hole_thermodynamics" title="Black hole thermodynamics">Black hole thermodynamics</a></li> <li><a href="/wiki/Unparticle_physics" title="Unparticle physics">Unparticle physics</a></li> <li><a href="/wiki/Graviphoton" title="Graviphoton">Graviphoton</a></li> <li><a href="/wiki/Graviscalar" title="Graviscalar">Graviscalar</a></li> <li><a href="/wiki/Graviton" title="Graviton">Graviton</a></li> <li><a href="/wiki/Gravitino" title="Gravitino">Gravitino</a></li> <li><a href="/wiki/Massive_gravity" title="Massive gravity">Massive gravity</a></li> <li><a href="/wiki/Gauge_gravitation_theory" title="Gauge gravitation theory">Gauge gravitation theory</a></li> <li><a href="/wiki/Gauge_theory_gravity" title="Gauge theory gravity">Gauge theory gravity</a></li> <li><a href="/wiki/CPT_symmetry" title="CPT symmetry">CPT symmetry</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible hlist"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;color: var(--color-base)"><a href="/wiki/Supersymmetry" title="Supersymmetry">Supersymmetry</a></div><div class="sidebar-list-content mw-collapsible-content plainlist"> <ul><li><a href="/wiki/Minimal_Supersymmetric_Standard_Model" title="Minimal Supersymmetric Standard Model">MSSM</a></li> <li><a href="/wiki/Next-to-Minimal_Supersymmetric_Standard_Model" title="Next-to-Minimal Supersymmetric Standard Model">NMSSM</a></li> <li><a href="/wiki/Superstring_theory" title="Superstring theory">Superstring theory</a></li> <li><a href="/wiki/M-theory" title="M-theory">M-theory</a></li> <li><a class="mw-selflink selflink">Supergravity</a></li> <li><a href="/wiki/Supersymmetry_breaking" title="Supersymmetry breaking">Supersymmetry breaking</a></li> <li><a href="/wiki/Extra_dimensions" title="Extra dimensions">Extra dimensions</a></li> <li><a href="/wiki/Large_extra_dimensions" title="Large extra dimensions">Large extra dimensions</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed hlist"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;color: var(--color-base)"><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a></div><div class="sidebar-list-content mw-collapsible-content plainlist"> <ul><li><a href="/wiki/False_vacuum" title="False vacuum">False vacuum</a></li> <li><a href="/wiki/String_theory" title="String theory">String theory</a></li> <li><a href="/wiki/Spin_foam" title="Spin foam">Spin foam</a></li> <li><a href="/wiki/Quantum_foam" title="Quantum foam">Quantum foam</a></li> <li><a href="/wiki/Quantum_geometry" title="Quantum geometry">Quantum geometry</a></li> <li><a href="/wiki/Loop_quantum_gravity" title="Loop quantum gravity">Loop quantum gravity</a></li> <li><a href="/wiki/Quantum_cosmology" title="Quantum cosmology">Quantum cosmology</a></li> <li><a href="/wiki/Loop_quantum_cosmology" title="Loop quantum cosmology">Loop quantum cosmology</a></li> <li><a href="/wiki/Causal_dynamical_triangulation" title="Causal dynamical triangulation">Causal dynamical triangulation</a></li> <li><a href="/wiki/Causal_fermion_systems" title="Causal fermion systems">Causal fermion systems</a></li> <li><a href="/wiki/Causal_sets" title="Causal sets">Causal sets</a></li> <li><a href="/wiki/Canonical_quantum_gravity" title="Canonical quantum gravity">Canonical quantum gravity</a></li> <li><a href="/wiki/Semiclassical_gravity" title="Semiclassical gravity">Semiclassical gravity</a></li> <li><a href="/wiki/Superfluid_vacuum_theory" title="Superfluid vacuum theory">Superfluid vacuum theory</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed hlist"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;color: var(--color-base)">Experiments</div><div class="sidebar-list-content mw-collapsible-content plainlist"> <ul><li><a href="/wiki/Accelerator_Neutrino_Neutron_Interaction_Experiment" title="Accelerator Neutrino Neutron Interaction Experiment">ANNIE</a></li> <li><a href="/wiki/Laboratori_Nazionali_del_Gran_Sasso" title="Laboratori Nazionali del Gran Sasso">Gran Sasso</a></li> <li><a href="/wiki/India-based_Neutrino_Observatory" title="India-based Neutrino Observatory">INO</a></li> <li><a href="/wiki/Large_Hadron_Collider" title="Large Hadron Collider">LHC</a></li> <li><a href="/wiki/Sudbury_Neutrino_Observatory" title="Sudbury Neutrino Observatory">SNO</a></li> <li><a href="/wiki/Super-Kamiokande" title="Super-Kamiokande">Super-K</a></li> <li><a href="/wiki/Tevatron" title="Tevatron">Tevatron</a></li> <li><a href="/wiki/NOvA" title="NOvA">NOvA</a></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output 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class="sidebar-title"><a href="/wiki/String_theory" title="String theory">String theory</a></th></tr><tr><td class="sidebar-image"><span typeof="mw:File/Frameless"><a href="/wiki/File:Calabi_yau_formatted.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Calabi_yau_formatted.svg/100px-Calabi_yau_formatted.svg.png" decoding="async" width="100" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Calabi_yau_formatted.svg/150px-Calabi_yau_formatted.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Calabi_yau_formatted.svg/200px-Calabi_yau_formatted.svg.png 2x" data-file-width="215" data-file-height="224" /></a></span></td></tr><tr><th class="sidebar-heading" style="background: #ddf"> Fundamental objects</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/String_(physics)" title="String (physics)">String</a></li> <li><a href="/wiki/Cosmic_string" title="Cosmic string">Cosmic string</a></li> <li><a href="/wiki/Brane" title="Brane">Brane</a></li> <li><a href="/wiki/D-brane" title="D-brane">D-brane</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background: #ddf"> Perturbative theory</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Bosonic_string_theory" title="Bosonic string theory">Bosonic</a></li> <li><a href="/wiki/Superstring_theory" title="Superstring theory">Superstring</a> (<a href="/wiki/Type_I_string_theory" title="Type I string theory">Type I</a>, <a href="/wiki/Type_II_string_theory" title="Type II string theory">Type II</a>, <a href="/wiki/Heterotic_string_theory" title="Heterotic string theory">Heterotic</a>)</li></ul></td> </tr><tr><th class="sidebar-heading" style="background: #ddf"> Non-perturbative results</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/S-duality" title="S-duality">S-duality</a></li> <li><a href="/wiki/T-duality" title="T-duality">T-duality</a></li> <li><a href="/wiki/U-duality" title="U-duality">U-duality</a></li> <li><a href="/wiki/M-theory" title="M-theory">M-theory</a></li> <li><a href="/wiki/F-theory" title="F-theory">F-theory</a></li> <li><a href="/wiki/AdS/CFT_correspondence" title="AdS/CFT correspondence">AdS/CFT correspondence</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background: #ddf"> Phenomenology</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/String_phenomenology" title="String phenomenology">Phenomenology</a></li> <li><a href="/wiki/String_cosmology" title="String cosmology">Cosmology</a></li> <li><a href="/wiki/String_theory_landscape" title="String theory landscape">Landscape</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background: #ddf"> Mathematics</th></tr><tr><td class="sidebar-content" style="padding-bottom:0.75em;"> <ul><li><a href="/wiki/Geometric_Langlands_correspondence" title="Geometric Langlands correspondence">Geometric Langlands correspondence</a></li> <li><a href="/wiki/Mirror_symmetry_(string_theory)" title="Mirror symmetry (string theory)">Mirror symmetry</a></li> <li><a href="/wiki/Monstrous_moonshine" title="Monstrous moonshine">Monstrous moonshine</a></li> <li><a href="/wiki/Vertex_algebra" class="mw-redirect" title="Vertex algebra">Vertex algebra</a></li> <li><a href="/wiki/K-theory_(physics)" title="K-theory (physics)">K-theory</a></li></ul></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background: #ddf; text-align:center;;color: var(--color-base)">Related concepts</div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"> <ul><li><a href="/wiki/Theory_of_everything" title="Theory of everything">Theory of everything</a></li> <li><a href="/wiki/Conformal_field_theory" title="Conformal field theory">Conformal field theory</a></li> <li><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a></li> <li><a href="/wiki/Supersymmetry" title="Supersymmetry">Supersymmetry</a></li> <li><a class="mw-selflink selflink">Supergravity</a></li> <li><a href="/wiki/Twistor_string_theory" title="Twistor string theory">Twistor string theory</a></li> <li><a href="/wiki/N_%3D_4_supersymmetric_Yang%E2%80%93Mills_theory" title="N = 4 supersymmetric Yang–Mills theory"><i>N</i> = 4 supersymmetric Yang–Mills theory</a></li> <li><a href="/wiki/Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein theory</a></li> <li><a href="/wiki/Multiverse" title="Multiverse">Multiverse</a></li> <li><a href="/wiki/Holographic_principle" title="Holographic principle">Holographic principle</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background: #ddf; text-align:center;;color: var(--color-base)">Theorists</div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"> <ul><li><a href="/wiki/Mina_Aganagi%C4%87" title="Mina Aganagić">Aganagić</a></li> <li><a href="/wiki/Nima_Arkani-Hamed" title="Nima Arkani-Hamed">Arkani-Hamed</a></li> <li><a href="/wiki/Michael_Atiyah" title="Michael Atiyah">Atiyah</a></li> <li><a href="/wiki/Tom_Banks_(physicist)" title="Tom Banks (physicist)">Banks</a></li> <li><a href="/wiki/David_Berenstein" title="David Berenstein">Berenstein</a></li> <li><a href="/wiki/Raphael_Bousso" title="Raphael Bousso">Bousso</a></li> <li><a href="/wiki/Thomas_Curtright" title="Thomas Curtright">Curtright</a></li> <li><a href="/wiki/Robbert_Dijkgraaf" title="Robbert Dijkgraaf">Dijkgraaf</a></li> <li><a href="/wiki/Jacques_Distler" title="Jacques Distler">Distler</a></li> <li><a href="/wiki/Michael_R._Douglas" title="Michael R. Douglas">Douglas</a></li> <li><a href="/wiki/Michael_Duff_(physicist)" title="Michael Duff (physicist)">Duff</a></li> <li><a href="/wiki/Gia_Dvali" class="mw-redirect" title="Gia Dvali">Dvali</a></li> <li><a href="/wiki/Sergio_Ferrara" title="Sergio Ferrara">Ferrara</a></li> <li><a href="/wiki/Willy_Fischler" title="Willy Fischler">Fischler</a></li> <li><a href="/wiki/Daniel_Friedan" title="Daniel Friedan">Friedan</a></li> <li><a href="/wiki/Sylvester_James_Gates" title="Sylvester James Gates">Gates</a></li> <li><a href="/wiki/Ferdinando_Gliozzi" title="Ferdinando Gliozzi">Gliozzi</a></li> <li><a href="/wiki/Rajesh_Gopakumar" title="Rajesh Gopakumar">Gopakumar</a></li> <li><a href="/wiki/Michael_Green_(physicist)" title="Michael Green (physicist)">Green</a></li> <li><a href="/wiki/Brian_Greene" title="Brian Greene">Greene</a></li> <li><a href="/wiki/David_Gross" title="David Gross">Gross</a></li> <li><a href="/wiki/Steven_Gubser" title="Steven Gubser">Gubser</a></li> <li><a href="/wiki/Sergei_Gukov" title="Sergei Gukov">Gukov</a></li> <li><a href="/wiki/Alan_Guth" title="Alan Guth">Guth</a></li> <li><a href="/wiki/Andrew_J._Hanson" title="Andrew J. Hanson">Hanson</a></li> <li><a href="/wiki/Jeffrey_A._Harvey" title="Jeffrey A. Harvey">Harvey</a></li> <li><a href="/wiki/Petr_Ho%C5%99ava_(theorist)" class="mw-redirect" title="Petr Hořava (theorist)">Hořava</a></li> <li><a href="/wiki/Gary_Horowitz" title="Gary Horowitz">Horowitz</a></li> <li><a href="/wiki/Gary_Gibbons" title="Gary Gibbons">Gibbons</a></li> <li><a href="/wiki/Shamit_Kachru" title="Shamit Kachru">Kachru</a></li> <li><a href="/wiki/Michio_Kaku" title="Michio Kaku">Kaku</a></li> <li><a href="/wiki/Renata_Kallosh" title="Renata Kallosh">Kallosh</a></li> <li><a href="/wiki/Theodor_Kaluza" title="Theodor Kaluza">Kaluza</a></li> <li><a href="/wiki/Anton_Kapustin" title="Anton Kapustin">Kapustin</a></li> <li><a href="/wiki/Igor_Klebanov" title="Igor Klebanov">Klebanov</a></li> <li><a href="/wiki/Vadim_Knizhnik" title="Vadim Knizhnik">Knizhnik</a></li> <li><a href="/wiki/Maxim_Kontsevich" title="Maxim Kontsevich">Kontsevich</a></li> <li><a href="/wiki/Oskar_Klein" title="Oskar Klein">Klein</a></li> <li><a href="/wiki/Andrei_Linde" title="Andrei Linde">Linde</a></li> <li><a href="/wiki/Juan_Mart%C3%ADn_Maldacena" class="mw-redirect" title="Juan Martín Maldacena">Maldacena</a></li> <li><a href="/wiki/Stanley_Mandelstam" title="Stanley Mandelstam">Mandelstam</a></li> <li><a href="/wiki/Donald_Marolf" title="Donald Marolf">Marolf</a></li> <li><a href="/wiki/Emil_Martinec" title="Emil Martinec">Martinec</a></li> <li><a href="/wiki/Shiraz_Minwalla" title="Shiraz Minwalla">Minwalla</a></li> <li><a href="/wiki/Greg_Moore_(physicist)" title="Greg Moore (physicist)">Moore</a></li> <li><a href="/wiki/Lubo%C5%A1_Motl" title="Luboš Motl">Motl</a></li> <li><a href="/wiki/Sunil_Mukhi" title="Sunil Mukhi">Mukhi</a></li> <li><a href="/wiki/Robert_Myers_(physicist)" title="Robert Myers (physicist)">Myers</a></li> <li><a href="/wiki/Dimitri_Nanopoulos" title="Dimitri Nanopoulos">Nanopoulos</a></li> <li><a href="/wiki/Hora%C8%9Biu_N%C4%83stase" title="Horațiu Năstase">Năstase</a></li> <li><a href="/wiki/Nikita_Nekrasov" title="Nikita Nekrasov">Nekrasov</a></li> <li><a href="/wiki/Andr%C3%A9_Neveu" title="André Neveu">Neveu</a></li> <li><a href="/wiki/Holger_Bech_Nielsen" title="Holger Bech Nielsen">Nielsen</a></li> <li><a href="/wiki/Peter_van_Nieuwenhuizen" title="Peter van Nieuwenhuizen">van Nieuwenhuizen</a></li> <li><a href="/wiki/Sergei_Novikov_(mathematician)" title="Sergei Novikov (mathematician)">Novikov</a></li> <li><a href="/wiki/David_Olive" title="David Olive">Olive</a></li> <li><a href="/wiki/Hirosi_Ooguri" title="Hirosi Ooguri">Ooguri</a></li> <li><a href="/wiki/Burt_Ovrut" title="Burt Ovrut">Ovrut</a></li> <li><a href="/wiki/Joseph_Polchinski" title="Joseph Polchinski">Polchinski</a></li> <li><a href="/wiki/Alexander_Markovich_Polyakov" title="Alexander Markovich Polyakov">Polyakov</a></li> <li><a href="/wiki/Arvind_Rajaraman" title="Arvind Rajaraman">Rajaraman</a></li> <li><a href="/wiki/Pierre_Ramond" title="Pierre Ramond">Ramond</a></li> <li><a href="/wiki/Lisa_Randall" title="Lisa Randall">Randall</a></li> <li><a href="/wiki/Seifallah_Randjbar-Daemi" title="Seifallah Randjbar-Daemi">Randjbar-Daemi</a></li> <li><a href="/wiki/Martin_Ro%C4%8Dek" title="Martin Roček">Roček</a></li> <li><a href="/wiki/Ryan_Rohm" title="Ryan Rohm">Rohm</a></li> <li><a href="/wiki/Augusto_Sagnotti" title="Augusto Sagnotti">Sagnotti</a></li> <li><a href="/wiki/Jo%C3%ABl_Scherk" title="Joël Scherk">Scherk</a></li> <li><a href="/wiki/John_Henry_Schwarz" title="John Henry Schwarz">Schwarz</a></li> <li><a href="/wiki/Nathan_Seiberg" title="Nathan Seiberg">Seiberg</a></li> <li><a href="/wiki/Ashoke_Sen" title="Ashoke Sen">Sen</a></li> <li><a href="/wiki/Stephen_Shenker" title="Stephen Shenker">Shenker</a></li> <li><a href="/wiki/Warren_Siegel" title="Warren Siegel">Siegel</a></li> <li><a href="/wiki/Eva_Silverstein" title="Eva Silverstein">Silverstein</a></li> <li><a href="/wiki/%C4%90%C3%A0m_Thanh_S%C6%A1n" title="Đàm Thanh Sơn">Sơn</a></li> <li><a href="/wiki/Matthias_Staudacher" title="Matthias Staudacher">Staudacher</a></li> <li><a href="/wiki/Paul_Steinhardt" title="Paul Steinhardt">Steinhardt</a></li> <li><a href="/wiki/Andrew_Strominger" title="Andrew Strominger">Strominger</a></li> <li><a href="/wiki/Raman_Sundrum" title="Raman Sundrum">Sundrum</a></li> <li><a href="/wiki/Leonard_Susskind" title="Leonard Susskind">Susskind</a></li> <li><a href="/wiki/Gerard_%27t_Hooft" title="Gerard 't Hooft">'t Hooft</a></li> <li><a href="/wiki/Paul_Townsend" title="Paul Townsend">Townsend</a></li> <li><a href="/wiki/Sandip_Trivedi" title="Sandip Trivedi">Trivedi</a></li> <li><a href="/wiki/Neil_Turok" title="Neil Turok">Turok</a></li> <li><a href="/wiki/Cumrun_Vafa" title="Cumrun Vafa">Vafa</a></li> <li><a href="/wiki/Gabriele_Veneziano" title="Gabriele Veneziano">Veneziano</a></li> <li><a href="/wiki/Erik_Verlinde" title="Erik Verlinde">Verlinde</a></li> <li><a href="/wiki/Herman_Verlinde" title="Herman Verlinde">Verlinde</a></li> <li><a href="/wiki/Julius_Wess" title="Julius Wess">Wess</a></li> <li><a href="/wiki/Edward_Witten" title="Edward Witten">Witten</a></li> <li><a href="/wiki/Shing-Tung_Yau" title="Shing-Tung Yau">Yau</a></li> <li><a href="/wiki/Tamiaki_Yoneya" title="Tamiaki Yoneya">Yoneya</a></li> <li><a href="/wiki/Alexander_Zamolodchikov" title="Alexander Zamolodchikov">Zamolodchikov</a></li> <li><a href="/wiki/Alexei_Zamolodchikov" title="Alexei Zamolodchikov">Zamolodchikov</a></li> <li><a href="/wiki/Eric_Zaslow" title="Eric Zaslow">Zaslow</a></li> <li><a href="/wiki/Bruno_Zumino" title="Bruno Zumino">Zumino</a></li> <li><a href="/wiki/Barton_Zwiebach" title="Barton Zwiebach">Zwiebach</a></li></ul></div></div></td> </tr><tr><td class="sidebar-below hlist" style="display:block;margin-top:0.3em;"> <ul><li><a href="/wiki/History_of_string_theory" title="History of string theory">History</a></li> <li><a href="/wiki/Glossary_of_string_theory" title="Glossary of string theory">Glossary</a></li></ul></td></tr><tr><td class="sidebar-navbar" style="padding-top:0.25em;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:String_theory" title="Template:String theory"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:String_theory" title="Template talk:String theory"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:String_theory" title="Special:EditPage/Template:String theory"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>In <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physics</a>, <b>supergravity</b> (<b>supergravity theory</b>; <b>SUGRA</b> for short) is a modern <a href="/wiki/Field_theory_(physics)" class="mw-redirect" title="Field theory (physics)">field theory</a> that combines the principles of <a href="/wiki/Supersymmetry" title="Supersymmetry">supersymmetry</a> and <a href="/wiki/General_relativity" title="General relativity">general relativity</a>; this is in contrast to non-gravitational supersymmetric theories such as the <a href="/wiki/Minimal_Supersymmetric_Standard_Model" title="Minimal Supersymmetric Standard Model">Minimal Supersymmetric Standard Model</a>. Supergravity is the <a href="/wiki/Gauge_theory" title="Gauge theory">gauge theory</a> of local supersymmetry. Since the supersymmetry (SUSY) generators form together with the <a href="/wiki/Poincar%C3%A9_algebra" class="mw-redirect" title="Poincaré algebra">Poincaré algebra</a> a <a href="/wiki/Superalgebra" title="Superalgebra">superalgebra</a>, called the <a href="/wiki/Super-Poincar%C3%A9_algebra" title="Super-Poincaré algebra">super-Poincaré algebra</a>, supersymmetry as a gauge theory makes gravity arise in a natural way.<sup id="cite_ref-Niewwenhuizen_1-0" class="reference"><a href="#cite_note-Niewwenhuizen-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Gravitons">Gravitons</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Supergravity&action=edit&section=1" title="Edit section: Gravitons"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Like all covariant approaches to quantum gravity,<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> supergravity contains a spin-2 field whose quantum is the <a href="/wiki/Graviton" title="Graviton">graviton</a>. Supersymmetry requires the graviton field to have a <a href="/wiki/Superpartner" title="Superpartner">superpartner</a>. This field has <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a> 3/2 and its quantum is the <a href="/wiki/Gravitino" title="Gravitino">gravitino</a>. The number of gravitino fields is equal to the number of supersymmetries. </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Supergravity&action=edit&section=2" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Gauge_supersymmetry">Gauge supersymmetry</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Supergravity&action=edit&section=3" title="Edit section: Gauge supersymmetry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The first theory of local supersymmetry was proposed by <a href="/wiki/Richard_Arnowitt" title="Richard Arnowitt">Dick Arnowitt</a> and <a href="/wiki/Pran_Nath_(physicist)" title="Pran Nath (physicist)">Pran Nath</a> in 1975<sup id="cite_ref-NathArnowitt_3-0" class="reference"><a href="#cite_note-NathArnowitt-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> and was called <b>gauge supersymmetry</b>. </p> <div class="mw-heading mw-heading3"><h3 id="Supergravity">Supergravity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Supergravity&action=edit&section=4" title="Edit section: Supergravity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The first model of 4-dimensional supergravity (without this denotation) was formulated by Dmitri Vasilievich Volkov and Vyacheslav A. Soroka in 1973,<sup id="cite_ref-Volkov_Soroka_4-0" class="reference"><a href="#cite_note-Volkov_Soroka-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> emphasizing the importance of spontaneous supersymmetry breaking for the possibility of a realistic model. The <a href="/wiki/Pure_4D_N_%3D_1_supergravity" title="Pure 4D N = 1 supergravity">minimal version of 4-dimensional supergravity</a> (with unbroken local supersymmetry) was constructed in detail in 1976 by <a href="/wiki/Daniel_Z._Freedman" title="Daniel Z. Freedman">Dan Freedman</a>, <a href="/wiki/Sergio_Ferrara" title="Sergio Ferrara">Sergio Ferrara</a> and <a href="/wiki/Peter_van_Nieuwenhuizen" title="Peter van Nieuwenhuizen">Peter van Nieuwenhuizen</a>.<sup id="cite_ref-Summary_5-0" class="reference"><a href="#cite_note-Summary-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> In 2019 the three were awarded a special <a href="/wiki/Breakthrough_Prize_in_Fundamental_Physics" title="Breakthrough Prize in Fundamental Physics">Breakthrough Prize in Fundamental Physics</a> for the discovery.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The key issue of whether or not the spin 3/2 field is consistently coupled was resolved in the nearly simultaneous paper, by <a href="/wiki/Stanley_Deser" title="Stanley Deser">Deser</a> and <a href="/wiki/Bruno_Zumino" title="Bruno Zumino">Zumino</a>,<sup id="cite_ref-DeserZumino_7-0" class="reference"><a href="#cite_note-DeserZumino-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> which independently proposed the minimal 4-dimensional model. It was quickly generalized to many different theories in various numbers of <a href="/wiki/Dimensions" class="mw-redirect" title="Dimensions">dimensions</a> and involving additional (N) supersymmetries. Supergravity theories with N>1 are usually referred to as extended supergravity (SUEGRA). Some supergravity theories were shown to be related to certain <a href="/wiki/Higher-dimensional" class="mw-redirect" title="Higher-dimensional">higher-dimensional</a> supergravity theories via <a href="/wiki/Compactification_(physics)" title="Compactification (physics)">dimensional reduction</a> (e.g. N=1, 11-dimensional supergravity is dimensionally reduced on T<sup>7</sup> to 4-dimensional, ungauged, <i>N</i> = 8 supergravity). The resulting theories were sometimes referred to as <a href="/wiki/Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein theories</a> as Kaluza and Klein constructed in 1919 a 5-dimensional gravitational theory, that when dimensionally reduced on a circle, its 4-dimensional non-massive modes describe <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a> coupled to <a href="/wiki/Gravity" title="Gravity">gravity</a>. </p> <div class="mw-heading mw-heading3"><h3 id="mSUGRA">mSUGRA</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Supergravity&action=edit&section=5" title="Edit section: mSUGRA"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>mSUGRA means minimal SUper GRAvity. The construction of a realistic model of particle interactions within the <i>N</i> = 1 supergravity framework where supersymmetry (SUSY) breaks by a super <a href="/wiki/Higgs_mechanism" title="Higgs mechanism">Higgs mechanism</a> carried out by <a href="/wiki/Ali_Chamseddine" title="Ali Chamseddine">Ali Chamseddine</a>, <a href="/wiki/Richard_Arnowitt" title="Richard Arnowitt">Richard Arnowitt</a> and <a href="/wiki/Pran_Nath_(physicist)" title="Pran Nath (physicist)">Pran Nath</a> in 1982. Collectively now known as minimal supergravity Grand Unification Theories (mSUGRA GUT), gravity mediates the breaking of SUSY through the existence of a <a href="/wiki/Hidden_sector" title="Hidden sector">hidden sector</a>. mSUGRA naturally generates the Soft SUSY breaking terms which are a consequence of the Super Higgs effect. Radiative breaking of electroweak symmetry through <a href="/wiki/Renormalization" title="Renormalization">Renormalization</a> Group Equations (RGEs) follows as an immediate consequence. Due to its predictive power, requiring only four input parameters and a sign to determine the low energy phenomenology from the scale of Grand Unification, its interest is a widely investigated model of <a href="/wiki/Particle_physics" title="Particle physics">particle physics</a> </p> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Minimal_Supersymmetric_Standard_Model#Gravity-mediated_supersymmetry_breaking" title="Minimal Supersymmetric Standard Model">Gravity-Mediated Supersymmetry Breaking in the MSSM</a></div> <div class="mw-heading mw-heading3"><h3 id="11D:_the_maximal_SUGRA">11D: the maximal SUGRA</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Supergravity&action=edit&section=6" title="Edit section: 11D: the maximal SUGRA"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Eleven-dimensional_supergravity" title="Eleven-dimensional supergravity">Eleven-dimensional supergravity</a></div> <p>One of these supergravities, the 11-dimensional theory, generated considerable excitement as the first potential candidate for the <a href="/wiki/Theory_of_everything" title="Theory of everything">theory of everything</a>. This excitement was built on four pillars, two of which have now been largely discredited: </p> <ul><li><a href="/wiki/Werner_Nahm" title="Werner Nahm">Werner Nahm</a> showed<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> 11 dimensions as the largest number of dimensions consistent with a single graviton, and more dimensions will show particles with spins greater than 2. However, if two of these dimensions are time-like, these problems are avoided in 12 dimensions. <a href="/wiki/Itzhak_Bars" title="Itzhak Bars">Itzhak Bars</a><sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2007)">citation needed</span></a></i>]</sup> gives this emphasis.</li> <li>In 1981 <a href="/wiki/Ed_Witten" class="mw-redirect" title="Ed Witten">Ed Witten</a> showed<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> 11 as the smallest number of dimensions big enough to contain the <a href="/wiki/Gauge_group" class="mw-redirect" title="Gauge group">gauge groups</a> of the <a href="/wiki/Standard_Model" title="Standard Model">Standard Model</a>, namely <a href="/wiki/SU(3)" class="mw-redirect" title="SU(3)">SU(3)</a> for the <a href="/wiki/Strong_interactions" class="mw-redirect" title="Strong interactions">strong interactions</a> and <a href="/wiki/SU(2)" class="mw-redirect" title="SU(2)">SU(2)</a> times <a href="/wiki/U(1)" class="mw-redirect" title="U(1)">U(1)</a> for the <a href="/wiki/Electroweak" class="mw-redirect" title="Electroweak">electroweak</a> interactions.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2013)">citation needed</span></a></i>]</sup> Many techniques exist to embed the standard model gauge group in supergravity in any number of dimensions like the obligatory gauge symmetry in <a href="/wiki/Type_I_string_theory" title="Type I string theory">type I</a> and <a href="/wiki/Heterotic_string_theory" title="Heterotic string theory">heterotic string theories</a>, and obtained in <a href="/wiki/Type_II_string_theory" title="Type II string theory">type II string theory</a> by <a href="/wiki/Compactification_(physics)" title="Compactification (physics)">compactification</a> on certain <a href="/wiki/Calabi%E2%80%93Yau_manifold" title="Calabi–Yau manifold">Calabi–Yau manifolds</a>. The <a href="/wiki/D-brane" title="D-brane">D-branes</a> engineer gauge symmetries too.</li> <li>In 1978 <a href="/wiki/Eug%C3%A8ne_Cremmer" title="Eugène Cremmer">Eugène Cremmer</a>, <a href="/wiki/Bernard_Julia" title="Bernard Julia">Bernard Julia</a> and <a href="/wiki/Jo%C3%ABl_Scherk" title="Joël Scherk">Joël Scherk</a> (CJS) found<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> the classical action for an 11-dimensional supergravity theory. This remains today the only known classical 11-dimensional theory with local supersymmetry and no fields of spin higher than two.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2007)">citation needed</span></a></i>]</sup> Other 11-dimensional theories known and quantum-mechanically inequivalent reduce to the CJS theory when one imposes the classical equations of motion. However, in the mid-1980s <a href="/wiki/Bernard_de_Wit" title="Bernard de Wit">Bernard de Wit</a> and <a href="/wiki/Hermann_Nicolai" title="Hermann Nicolai">Hermann Nicolai</a> found an alternate theory in D=11 Supergravity with Local SU(8) Invariance. While not manifestly Lorentz-invariant, it is in many ways superior, because it dimensionally-reduces to the 4-dimensional theory without recourse to the classical equations of motion.</li></ul> <ul><li>In 1980 <a href="/wiki/Peter_Freund" title="Peter Freund">Peter Freund</a> and <a href="/w/index.php?title=M._A._Rubin&action=edit&redlink=1" class="new" title="M. A. Rubin (page does not exist)">M. A. Rubin</a> showed that compactification from 11 dimensions preserving all the SUSY generators could occur in two ways, leaving only 4 or 7 macroscopic dimensions, the others compact.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The noncompact dimensions have to form an <a href="/wiki/Anti-de_Sitter_space" title="Anti-de Sitter space">anti-de Sitter space</a>. There are many possible compactifications, but the <a href="/wiki/Freund-Rubin_compactification" class="mw-redirect" title="Freund-Rubin compactification">Freund-Rubin compactification</a>'s invariance under all of the supersymmetry transformations preserves the action.</li></ul> <p>Finally, the first two results each appeared to establish 11 dimensions, the third result appeared to specify the theory, and the last result explained why the observed universe appears to be four-dimensional. </p><p>Many of the details of the theory were fleshed out by <a href="/wiki/Peter_van_Nieuwenhuizen" title="Peter van Nieuwenhuizen">Peter van Nieuwenhuizen</a>, <a href="/wiki/Sergio_Ferrara" title="Sergio Ferrara">Sergio Ferrara</a> and <a href="/wiki/Daniel_Z._Freedman" title="Daniel Z. Freedman">Daniel Z. Freedman</a>. </p> <div class="mw-heading mw-heading3"><h3 id="The_end_of_the_SUGRA_era">The end of the SUGRA era</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Supergravity&action=edit&section=7" title="Edit section: The end of the SUGRA era"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The initial excitement over 11-dimensional supergravity soon waned, as various failings were discovered, and attempts to repair the model failed as well. Problems included:<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2016)">citation needed</span></a></i>]</sup> </p> <ul><li>The compact manifolds which were known at the time and which contained the standard model were not compatible with supersymmetry, and could not hold <a href="/wiki/Quark" title="Quark">quarks</a> or <a href="/wiki/Lepton" title="Lepton">leptons</a>. One suggestion was to replace the compact dimensions with the 7-sphere, with the symmetry group <a href="/wiki/SO(8)" title="SO(8)">SO(8)</a>, or the squashed 7-sphere, with symmetry group <a href="/wiki/SO(5)" title="SO(5)">SO(5)</a> times <a href="/wiki/SU(2)" class="mw-redirect" title="SU(2)">SU(2)</a>.</li> <li>Until recently, the physical <a href="/wiki/Neutrino" title="Neutrino">neutrinos</a> seen in experiments were believed to be massless, and appeared to be left-handed, a phenomenon referred to as the <a href="/wiki/Chirality_(physics)" title="Chirality (physics)">chirality</a> of the Standard Model. It was very difficult to construct a chiral fermion from a compactification — the compactified manifold needed to have singularities, but physics near singularities did not begin to be understood until the advent of <a href="/wiki/Orbifold" title="Orbifold">orbifold</a> <a href="/wiki/Conformal_field_theory" title="Conformal field theory">conformal field theories</a> in the late 1980s.</li> <li>Supergravity models generically result in an unrealistically large <a href="/wiki/Cosmological_constant" title="Cosmological constant">cosmological constant</a> in four dimensions, and that constant is difficult to remove, and so require <a href="/wiki/Fine-tuning_(physics)" title="Fine-tuning (physics)">fine-tuning</a>. This is still a problem today.</li> <li>Quantization of the theory led to quantum field theory <a href="/wiki/Gauge_anomaly" title="Gauge anomaly">gauge anomalies</a> rendering the theory inconsistent. In the intervening years physicists have learned how to cancel these anomalies.</li></ul> <p>Some of these difficulties could be avoided by moving to a 10-dimensional theory involving <a href="/wiki/Superstring" class="mw-redirect" title="Superstring">superstrings</a>. However, by moving to 10 dimensions one loses the sense of uniqueness of the 11-dimensional theory.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>The core breakthrough for the 10-dimensional theory, known as the <a href="/wiki/First_superstring_revolution" class="mw-redirect" title="First superstring revolution">first superstring revolution</a>, was a demonstration by <a href="/wiki/Michael_B._Green" class="mw-redirect" title="Michael B. Green">Michael B. Green</a>, <a href="/wiki/John_H._Schwarz" class="mw-redirect" title="John H. Schwarz">John H. Schwarz</a> and <a href="/wiki/David_Gross" title="David Gross">David Gross</a> that there are only three supergravity models in 10 dimensions which have gauge symmetries and in which all of the gauge and <a href="/wiki/Gravitational_anomalies" class="mw-redirect" title="Gravitational anomalies">gravitational anomalies</a> cancel. These were theories built on the groups <a href="/wiki/SO(32)" class="mw-redirect" title="SO(32)">SO(32)</a> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{8}\times E_{8}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> <mo>×</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{8}\times E_{8}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b9008d94ef63220f6c67e484f60489e7ef2f550" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.379ex; height:2.509ex;" alt="{\displaystyle E_{8}\times E_{8}}"></span>, the <a href="/wiki/Direct_product_of_groups" title="Direct product of groups">direct product</a> of two copies of <a href="/wiki/E8_(mathematics)" title="E8 (mathematics)">E<sub>8</sub></a>. Today we know that, using <a href="/wiki/D-branes" class="mw-redirect" title="D-branes">D-branes</a> for example, gauge symmetries can be introduced in other 10-dimensional theories as well.<sup id="cite_ref-Blumen_13-0" class="reference"><a href="#cite_note-Blumen-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="The_second_superstring_revolution">The second superstring revolution</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Supergravity&action=edit&section=8" title="Edit section: The second superstring revolution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Initial excitement about the 10-dimensional theories, and the string theories that provide their quantum completion, died by the end of the 1980s. There were too many <a href="/wiki/Calabi%E2%80%93Yau" class="mw-redirect" title="Calabi–Yau">Calabi–Yaus</a> to compactify on, many more than <a href="/wiki/Shing-Tung_Yau" title="Shing-Tung Yau">Yau</a> had estimated, as he admitted in December 2005 at the <a href="/wiki/23rd_International_Solvay_Conference_in_Physics" class="mw-redirect" title="23rd International Solvay Conference in Physics">23rd International Solvay Conference in Physics</a>. None quite gave the standard model, but it seemed as though one could get close with enough effort in many distinct ways. Plus no one understood the theory beyond the regime of applicability of string <a href="/wiki/Perturbation_theory" title="Perturbation theory">perturbation theory</a>. </p><p>There was a comparatively quiet period at the beginning of the 1990s; however, several important tools were developed. For example, it became apparent that the various superstring theories were related by "<a href="/wiki/String_dualities" class="mw-redirect" title="String dualities">string dualities</a>", some of which relate weak string-coupling - perturbative - physics in one model with strong string-coupling - non-perturbative - in another. </p><p>Then the <a href="/wiki/Second_superstring_revolution" class="mw-redirect" title="Second superstring revolution">second superstring revolution</a> occurred. <a href="/wiki/Joseph_Polchinski" title="Joseph Polchinski">Joseph Polchinski</a> realized that obscure string theory objects, called <a href="/wiki/D-branes" class="mw-redirect" title="D-branes">D-branes</a>, which he discovered six years earlier, equate to stringy versions of the <a href="/wiki/P-branes" class="mw-redirect" title="P-branes">p-branes</a> known in supergravity theories. String theory perturbation didn't restrict these <a href="/wiki/P-branes" class="mw-redirect" title="P-branes">p-branes</a>. Thanks to supersymmetry, p-branes in supergravity gained understanding well beyond the limits of string theory. </p><p>Armed with this new <a href="/wiki/Nonperturbative" class="mw-redirect" title="Nonperturbative">nonperturbative</a> tool, <a href="/wiki/Edward_Witten" title="Edward Witten">Edward Witten</a> and many others could show all of the perturbative string theories as descriptions of different states in a single theory that Witten named <a href="/wiki/M-theory" title="M-theory">M-theory</a>. Furthermore, he argued that M-theory's <a href="/wiki/Long_Wavelength_Limit" class="mw-redirect" title="Long Wavelength Limit">long wavelength limit</a>, i.e. when the quantum wavelength associated to objects in the theory appear much larger than the size of the 11th dimension, needs 11-dimensional supergravity descriptors that fell out of favor with the <a href="/wiki/First_superstring_revolution" class="mw-redirect" title="First superstring revolution">first superstring revolution</a> 10 years earlier, accompanied by the 2- and 5-branes. </p><p>Therefore, supergravity comes full circle and uses a common framework in understanding features of string theories, M-theory, and their compactifications to lower spacetime dimensions. </p> <div class="mw-heading mw-heading2"><h2 id="Relation_to_superstrings">Relation to superstrings</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Supergravity&action=edit&section=9" title="Edit section: Relation to superstrings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The term "low energy limits" labels some 10-dimensional supergravity theories. These arise as the massless, <a href="/wiki/Tree_(graph_theory)" title="Tree (graph theory)">tree</a>-level approximation of string theories. True <a href="/wiki/Effective_field_theories" class="mw-redirect" title="Effective field theories">effective field theories</a> of string theories, rather than truncations, are rarely available. Due to string dualities, the conjectured 11-dimensional M-theory is required to have 11-dimensional supergravity as a "low energy limit". However, this doesn't necessarily mean that string theory/M-theory is the only possible <a href="/wiki/UV_completion" class="mw-redirect" title="UV completion">UV completion</a> of supergravity;<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2007)">citation needed</span></a></i>]</sup> supergravity research is useful independent of those relations. </p> <div class="mw-heading mw-heading2"><h2 id="4D_N_=_1_SUGRA"><span id="4D_N_.3D_1_SUGRA"></span>4D <i>N</i> = 1 SUGRA</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Supergravity&action=edit&section=10" title="Edit section: 4D N = 1 SUGRA"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/4D_N_%3D_1_supergravity" title="4D N = 1 supergravity">4D N = 1 supergravity</a></div> <p>Before we move on to SUGRA proper, let's recapitulate some important details about general relativity. We have a 4D differentiable manifold M with a Spin(3,1) principal bundle over it. This principal bundle represents the local Lorentz symmetry. In addition, we have a vector bundle T over the manifold with the fiber having four real dimensions and transforming as a vector under Spin(3,1). We have an invertible linear map from the tangent bundle TM<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Avoid_weasel_words" class="mw-redirect" title="Wikipedia:Avoid weasel words"><span title="The material near this tag possibly uses too vague attribution or weasel words. (February 2021)">which?</span></a></i>]</sup> to T. This map is the <a href="/wiki/Vierbein" class="mw-redirect" title="Vierbein">vierbein</a>. The local Lorentz symmetry has a <a href="/wiki/Gauge_connection" class="mw-redirect" title="Gauge connection">gauge connection</a> associated with it, the <a href="/wiki/Spin_connection" title="Spin connection">spin connection</a>. </p><p>The following discussion will be in superspace notation, as opposed to the component notation, which isn't manifestly covariant under SUSY. There are actually <i>many</i> different versions of SUGRA out there which are inequivalent in the sense that their actions and constraints upon the torsion tensor are different, but ultimately equivalent in that we can always perform a field redefinition of the supervierbeins and spin connection to get from one version to another. </p><p>In 4D N=1 SUGRA, we have a 4|4 real differentiable supermanifold M, i.e. we have 4 real bosonic dimensions and 4 real fermionic dimensions. As in the nonsupersymmetric case, we have a Spin(3,1) principal bundle over M. We have an <b>R</b><sup>4|4</sup> vector bundle T over M. The fiber of T transforms under the local Lorentz group as follows; the four real bosonic dimensions transform as a vector and the four real fermionic dimensions transform as a <a href="/wiki/Majorana_equation" title="Majorana equation">Majorana spinor</a>. This Majorana spinor can be reexpressed as a complex left-handed Weyl spinor and its complex conjugate right-handed <a href="/wiki/Weyl_equation" title="Weyl equation">Weyl spinor</a> (they're not independent of each other). We also have a spin connection as before. </p><p>We will use the following conventions; the spatial (both bosonic and fermionic) indices will be indicated by M, N, ... . The bosonic spatial indices will be indicated by μ, ν, ..., the left-handed Weyl spatial indices by α, β,..., and the right-handed Weyl spatial indices by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {\alpha }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo>˙</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {\alpha }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/beb4dcd8d1ac382ed357769dc1bf9f90e5f9c36a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:2.176ex;" alt="{\displaystyle {\dot {\alpha }}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {\beta }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>β</mi> <mo>˙</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {\beta }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/650de290a4d676fdb17ceda7cd05fa85b0dc7353" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.451ex; height:3.176ex;" alt="{\displaystyle {\dot {\beta }}}"></span>, ... . The indices for the fiber of T will follow a similar notation, except that they will be hatted like this: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {M}},{\hat {\alpha }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>M</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {M}},{\hat {\alpha }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5e322e0c6f680122c0f43061dfa3b053df4188c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.964ex; height:3.176ex;" alt="{\displaystyle {\hat {M}},{\hat {\alpha }}}"></span>. See <a href="/wiki/Van_der_Waerden_notation" title="Van der Waerden notation">van der Waerden notation</a> for more details. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M=(\mu ,\alpha ,{\dot {\alpha }})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mi>μ</mi> <mo>,</mo> <mi>α</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M=(\mu ,\alpha ,{\dot {\alpha }})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/185caed9193d74bf0e2e6f4f116f676a845a1099" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.795ex; height:2.843ex;" alt="{\displaystyle M=(\mu ,\alpha ,{\dot {\alpha }})}"></span>. The supervierbein is denoted by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e_{N}^{\hat {M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>M</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e_{N}^{\hat {M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2189d9c7ebad2a276a246a77b721fc5a5151b278" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.043ex; height:3.676ex;" alt="{\displaystyle e_{N}^{\hat {M}}}"></span>, and the spin connection by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{{\hat {M}}{\hat {N}}P}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>M</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>N</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mi>P</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{{\hat {M}}{\hat {N}}P}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47030368ae7d566350cb27b1b4404a9399cb4b2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:6.098ex; height:2.509ex;" alt="{\displaystyle \omega _{{\hat {M}}{\hat {N}}P}}"></span>. The <i>inverse</i> supervierbein is denoted by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\hat {M}}^{N}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>M</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\hat {M}}^{N}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e97de97228b7b211ccfa1a3c2bf745502b8077c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:3.674ex; height:3.676ex;" alt="{\displaystyle E_{\hat {M}}^{N}}"></span>. </p><p>The supervierbein and spin connection are real in the sense that they satisfy the reality conditions </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e_{N}^{\hat {M}}(x,{\overline {\theta }},\theta )^{*}=e_{N^{*}}^{{\hat {M}}^{*}}(x,\theta ,{\overline {\theta }})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>M</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msubsup> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>θ</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo>,</mo> <mi>θ</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <msubsup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>M</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mrow> </msubsup> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>θ</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>θ</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e_{N}^{\hat {M}}(x,{\overline {\theta }},\theta )^{*}=e_{N^{*}}^{{\hat {M}}^{*}}(x,\theta ,{\overline {\theta }})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/185c5837254ba0f6e177b16174336459d8690fe4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:26.075ex; height:4.009ex;" alt="{\displaystyle e_{N}^{\hat {M}}(x,{\overline {\theta }},\theta )^{*}=e_{N^{*}}^{{\hat {M}}^{*}}(x,\theta ,{\overline {\theta }})}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu ^{*}=\mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu ^{*}=\mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec89713906773bd53c5a08f5deab5a30d626c88b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.956ex; height:2.843ex;" alt="{\displaystyle \mu ^{*}=\mu }"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ^{*}={\dot {\alpha }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo>˙</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ^{*}={\dot {\alpha }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb4633e7e5dbe9c53f7e717be8768ddd3a657993" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.128ex; height:2.343ex;" alt="{\displaystyle \alpha ^{*}={\dot {\alpha }}}"></span>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {\alpha }}^{*}=\alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {\alpha }}^{*}=\alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/afdaf8a205e5a280e4af739ed8a5c0d58302f673" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.128ex; height:2.343ex;" alt="{\displaystyle {\dot {\alpha }}^{*}=\alpha }"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega (x,{\overline {\theta }},\theta )^{*}=\omega (x,\theta ,{\overline {\theta }})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>θ</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo>,</mo> <mi>θ</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <mi>ω</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>θ</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>θ</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega (x,{\overline {\theta }},\theta )^{*}=\omega (x,\theta ,{\overline {\theta }})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2692d77b9405a1e0a15ade3ddebd014bdc7a9dea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.05ex; height:3.509ex;" alt="{\displaystyle \omega (x,{\overline {\theta }},\theta )^{*}=\omega (x,\theta ,{\overline {\theta }})}"></span>.</dd></dl> <p>The <a href="/wiki/Covariant_derivative" title="Covariant derivative">covariant derivative</a> is defined as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{\hat {M}}f=E_{\hat {M}}^{N}\left(\partial _{N}f+\omega _{N}[f]\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>M</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msub> <mi>f</mi> <mo>=</mo> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>M</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mrow> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mi>f</mi> <mo>+</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mo stretchy="false">[</mo> <mi>f</mi> <mo stretchy="false">]</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{\hat {M}}f=E_{\hat {M}}^{N}\left(\partial _{N}f+\omega _{N}[f]\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2206a31f5837b4aeb2bcd523179c3bb5de2f5e4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:26.886ex; height:3.676ex;" alt="{\displaystyle D_{\hat {M}}f=E_{\hat {M}}^{N}\left(\partial _{N}f+\omega _{N}[f]\right)}"></span>.</dd></dl> <p>The <a href="/wiki/Covariant_exterior_derivative" class="mw-redirect" title="Covariant exterior derivative">covariant exterior derivative</a> as defined over supermanifolds needs to be super graded. This means that every time we interchange two fermionic indices, we pick up a +1 sign factor, instead of -1. </p><p>The presence or absence of <a href="/wiki/R-symmetry" title="R-symmetry">R symmetries</a> is optional, but if R-symmetry exists, the integrand over the full superspace has to have an R-charge of 0 and the integrand over chiral superspace has to have an R-charge of 2. </p><p>A chiral superfield <i>X</i> is a superfield which satisfies <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overline {D}}_{\hat {\dot {\alpha }}}X=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msub> <mi>X</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {D}}_{\hat {\dot {\alpha }}}X=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/977df4451e2a20a74db8f8cde2c34bc7a53ddec3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:9.564ex; height:4.176ex;" alt="{\displaystyle {\overline {D}}_{\hat {\dot {\alpha }}}X=0}"></span>. In order for this constraint to be consistent, we require the integrability conditions that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\{{\overline {D}}_{\hat {\dot {\alpha }}},{\overline {D}}_{\hat {\dot {\beta }}}\right\}=c_{{\hat {\dot {\alpha }}}{\hat {\dot {\beta }}}}^{\hat {\dot {\gamma }}}{\overline {D}}_{\hat {\dot {\gamma }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>{</mo> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>β</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msub> </mrow> <mo>}</mo> </mrow> <mo>=</mo> <msubsup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>β</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>γ</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msubsup> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>γ</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\{{\overline {D}}_{\hat {\dot {\alpha }}},{\overline {D}}_{\hat {\dot {\beta }}}\right\}=c_{{\hat {\dot {\alpha }}}{\hat {\dot {\beta }}}}^{\hat {\dot {\gamma }}}{\overline {D}}_{\hat {\dot {\gamma }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/538df77a47ca744d06574dd12b661b6fa4446cbc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:20.449ex; height:5.676ex;" alt="{\displaystyle \left\{{\overline {D}}_{\hat {\dot {\alpha }}},{\overline {D}}_{\hat {\dot {\beta }}}\right\}=c_{{\hat {\dot {\alpha }}}{\hat {\dot {\beta }}}}^{\hat {\dot {\gamma }}}{\overline {D}}_{\hat {\dot {\gamma }}}}"></span> for some coefficients <i>c</i>. </p><p>Unlike nonSUSY GR, the <a href="/wiki/Torsion_tensor" title="Torsion tensor">torsion</a> has to be nonzero, at least with respect to the fermionic directions. Already, even in flat superspace, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{\hat {\alpha }}e_{\hat {\dot {\alpha }}}+{\overline {D}}_{\hat {\dot {\alpha }}}e_{\hat {\alpha }}\neq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msub> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msub> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msub> <mo>≠</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{\hat {\alpha }}e_{\hat {\dot {\alpha }}}+{\overline {D}}_{\hat {\dot {\alpha }}}e_{\hat {\alpha }}\neq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5524ff9986edf80f36abb5dfdd3f3b9285a11ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:18.368ex; height:4.176ex;" alt="{\displaystyle D_{\hat {\alpha }}e_{\hat {\dot {\alpha }}}+{\overline {D}}_{\hat {\dot {\alpha }}}e_{\hat {\alpha }}\neq 0}"></span>. In one version of SUGRA (but certainly not the only one), we have the following constraints upon the torsion tensor: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{{\hat {\underline {\alpha }}}{\hat {\underline {\beta }}}}^{\hat {\underline {\gamma }}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <munder> <mi>α</mi> <mo>_</mo> </munder> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <munder> <mi>β</mi> <mo>_</mo> </munder> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <munder> <mi>γ</mi> <mo>_</mo> </munder> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msubsup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{{\hat {\underline {\alpha }}}{\hat {\underline {\beta }}}}^{\hat {\underline {\gamma }}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41160baad2ff35fa8c5382b8bb600bf2a20eab59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.978ex; margin-bottom: -0.693ex; width:7.847ex; height:6.009ex;" alt="{\displaystyle T_{{\hat {\underline {\alpha }}}{\hat {\underline {\beta }}}}^{\hat {\underline {\gamma }}}=0}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{{\hat {\alpha }}{\hat {\beta }}}^{\hat {\mu }}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>β</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>μ</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msubsup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{{\hat {\alpha }}{\hat {\beta }}}^{\hat {\mu }}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc5146a7122c8fae292df724e69b074f7ea7f909" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.986ex; height:4.843ex;" alt="{\displaystyle T_{{\hat {\alpha }}{\hat {\beta }}}^{\hat {\mu }}=0}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{{\hat {\dot {\alpha }}}{\hat {\dot {\beta }}}}^{\hat {\mu }}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>β</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>μ</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msubsup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{{\hat {\dot {\alpha }}}{\hat {\dot {\beta }}}}^{\hat {\mu }}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a3b310a70868a8ddc50bd5adac7d808f2241835" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:7.986ex; height:5.343ex;" alt="{\displaystyle T_{{\hat {\dot {\alpha }}}{\hat {\dot {\beta }}}}^{\hat {\mu }}=0}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{{\hat {\alpha }}{\hat {\dot {\beta }}}}^{\hat {\mu }}=2i\sigma _{{\hat {\alpha }}{\hat {\dot {\beta }}}}^{\hat {\mu }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>β</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>μ</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msubsup> <mo>=</mo> <mn>2</mn> <mi>i</mi> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>β</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>μ</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{{\hat {\alpha }}{\hat {\dot {\beta }}}}^{\hat {\mu }}=2i\sigma _{{\hat {\alpha }}{\hat {\dot {\beta }}}}^{\hat {\mu }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc6684bc1989890b53a806c5694fb110a194949a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.482ex; height:5.343ex;" alt="{\displaystyle T_{{\hat {\alpha }}{\hat {\dot {\beta }}}}^{\hat {\mu }}=2i\sigma _{{\hat {\alpha }}{\hat {\dot {\beta }}}}^{\hat {\mu }}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{{\hat {\mu }}{\hat {\underline {\alpha }}}}^{\hat {\nu }}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>μ</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <munder> <mi>α</mi> <mo>_</mo> </munder> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ν</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msubsup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{{\hat {\mu }}{\hat {\underline {\alpha }}}}^{\hat {\nu }}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bcfbcb82a776c353d3623fddbd8be7350e8e078" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.518ex; margin-bottom: -0.653ex; width:7.895ex; height:4.676ex;" alt="{\displaystyle T_{{\hat {\mu }}{\hat {\underline {\alpha }}}}^{\hat {\nu }}=0}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{{\hat {\mu }}{\hat {\nu }}}^{\hat {\rho }}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>μ</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ν</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ρ</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </msubsup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{{\hat {\mu }}{\hat {\nu }}}^{\hat {\rho }}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e782dd8b92d548b43feb279c849fe9e8af3858c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:7.792ex; height:4.676ex;" alt="{\displaystyle T_{{\hat {\mu }}{\hat {\nu }}}^{\hat {\rho }}=0}"></span></dd></dl> <p>Here, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\underline {\alpha }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <munder> <mi>α</mi> <mo>_</mo> </munder> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\underline {\alpha }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ad21c6c6a881674db41689f55e62c3a769029f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.537ex; margin-bottom: -0.801ex; width:1.49ex; height:2.676ex;" alt="{\displaystyle {\underline {\alpha }}}"></span> is a shorthand notation to mean the index runs over either the left or right Weyl spinors. </p><p>The <a href="/wiki/Superdeterminant" class="mw-redirect" title="Superdeterminant">superdeterminant</a> of the supervierbein, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left|e\right|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mi>e</mi> <mo>|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left|e\right|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd0ac500c34f3ba52b31b6d16147271cdd8b4af4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.377ex; height:2.843ex;" alt="{\displaystyle \left|e\right|}"></span>, gives us the volume factor for M. Equivalently, we have the volume 4|4-superform<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e^{{\hat {\mu }}=0}\wedge \cdots \wedge e^{{\hat {\mu }}=3}\wedge e^{{\hat {\alpha }}=1}\wedge e^{{\hat {\alpha }}=2}\wedge e^{{\hat {\dot {\alpha }}}=1}\wedge e^{{\hat {\dot {\alpha }}}=2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>μ</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </msup> <mo>∧</mo> <mo>⋯</mo> <mo>∧</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>μ</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>=</mo> <mn>3</mn> </mrow> </msup> <mo>∧</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>=</mo> <mn>1</mn> </mrow> </msup> <mo>∧</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>=</mo> <mn>2</mn> </mrow> </msup> <mo>∧</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>=</mo> <mn>1</mn> </mrow> </msup> <mo>∧</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>=</mo> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e^{{\hat {\mu }}=0}\wedge \cdots \wedge e^{{\hat {\mu }}=3}\wedge e^{{\hat {\alpha }}=1}\wedge e^{{\hat {\alpha }}=2}\wedge e^{{\hat {\dot {\alpha }}}=1}\wedge e^{{\hat {\dot {\alpha }}}=2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/645fc189f907fa6f2dcdedd1259e19857fc4fe39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:44.906ex; height:3.509ex;" alt="{\displaystyle e^{{\hat {\mu }}=0}\wedge \cdots \wedge e^{{\hat {\mu }}=3}\wedge e^{{\hat {\alpha }}=1}\wedge e^{{\hat {\alpha }}=2}\wedge e^{{\hat {\dot {\alpha }}}=1}\wedge e^{{\hat {\dot {\alpha }}}=2}}"></span>. </p><p>If we complexify the superdiffeomorphisms, there is a gauge where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\hat {\dot {\alpha }}}^{\mu }=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msubsup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\hat {\dot {\alpha }}}^{\mu }=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/259e2e0994339ebce886e9f5b0bf7fd610167a66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.278ex; height:4.009ex;" alt="{\displaystyle E_{\hat {\dot {\alpha }}}^{\mu }=0}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\hat {\dot {\alpha }}}^{\beta }=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msubsup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\hat {\dot {\alpha }}}^{\beta }=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f85550a18632b1735b6472baf05858a82bff7e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.26ex; height:4.343ex;" alt="{\displaystyle E_{\hat {\dot {\alpha }}}^{\beta }=0}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\hat {\dot {\alpha }}}^{\dot {\beta }}=\delta _{\dot {\alpha }}^{\dot {\beta }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo>˙</mo> </mover> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>β</mi> <mo>˙</mo> </mover> </mrow> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>α</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>β</mi> <mo>˙</mo> </mover> </mrow> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\hat {\dot {\alpha }}}^{\dot {\beta }}=\delta _{\dot {\alpha }}^{\dot {\beta }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72062f93055478fc06f94d3d7280de3f4fd3a27e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:8.576ex; height:4.843ex;" alt="{\displaystyle E_{\hat {\dot {\alpha }}}^{\dot {\beta }}=\delta _{\dot {\alpha }}^{\dot {\beta }}}"></span>. The resulting chiral superspace has the coordinates x and Θ. </p><p><i>R</i> is a scalar valued chiral superfield derivable from the supervielbeins and spin connection. If <i>f</i> is any superfield, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\bar {D}}^{2}-8R\right)f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>8</mn> <mi>R</mi> </mrow> <mo>)</mo> </mrow> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\bar {D}}^{2}-8R\right)f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fb59cd3b27c5b4f67493f26dd5bb05b6bf9872a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.187ex; height:4.843ex;" alt="{\displaystyle \left({\bar {D}}^{2}-8R\right)f}"></span> is always a chiral superfield. </p><p>The action for a SUGRA theory with chiral superfields <i>X</i>, is given by </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S=\int d^{4}xd^{2}\Theta 2{\mathcal {E}}\left[{\frac {3}{8}}\left({\bar {D}}^{2}-8R\right)e^{-K({\bar {X}},X)/3}+W(X)\right]+c.c.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mo>∫</mo> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>x</mi> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi mathvariant="normal">Θ</mi> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mrow> <mo>[</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>8</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>8</mn> <mi>R</mi> </mrow> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>K</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>X</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>,</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mi>W</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> <mo>+</mo> <mi>c</mi> <mo>.</mo> <mi>c</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=\int d^{4}xd^{2}\Theta 2{\mathcal {E}}\left[{\frac {3}{8}}\left({\bar {D}}^{2}-8R\right)e^{-K({\bar {X}},X)/3}+W(X)\right]+c.c.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7c495b7c3e57bb0bd4d53830c4531a0e60196f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:60.306ex; height:6.176ex;" alt="{\displaystyle S=\int d^{4}xd^{2}\Theta 2{\mathcal {E}}\left[{\frac {3}{8}}\left({\bar {D}}^{2}-8R\right)e^{-K({\bar {X}},X)/3}+W(X)\right]+c.c.}"></span></dd></dl> <p>where <i>K</i> is the <a href="/wiki/K%C3%A4hler_potential" class="mw-redirect" title="Kähler potential">Kähler potential</a> and <i>W</i> is the <a href="/wiki/Superpotential" title="Superpotential">superpotential</a>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {E}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {E}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c298ed828ff778065aeb5f0f305097f55bb9ae0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.311ex; height:2.176ex;" alt="{\displaystyle {\mathcal {E}}}"></span> is the chiral volume factor. </p><p>Unlike the case for flat superspace, adding a constant to either the Kähler or superpotential is now physical. A constant shift to the Kähler potential changes the effective <a href="/wiki/Planck_constant" title="Planck constant">Planck constant</a>, while a constant shift to the superpotential changes the effective <a href="/wiki/Cosmological_constant" title="Cosmological constant">cosmological constant</a>. As the effective Planck constant now depends upon the value of the chiral superfield <i>X</i>, we need to rescale the supervierbeins (a field redefinition) to get a constant Planck constant. This is called the <b>Einstein frame</b>. </p> <div class="mw-heading mw-heading2"><h2 id="N_=_8_supergravity_in_4_dimensions"><span id="N_.3D_8_supergravity_in_4_dimensions"></span><i>N</i> = 8 supergravity in 4 dimensions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Supergravity&action=edit&section=11" title="Edit section: N = 8 supergravity in 4 dimensions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/N_%3D_8_supergravity" title="N = 8 supergravity"><i>N</i> = 8 supergravity</a> is the most <a href="/wiki/Symmetric" class="mw-redirect" title="Symmetric">symmetric</a> quantum field theory which involves gravity and a finite number of fields. It can be found from a dimensional reduction of 11D supergravity by making the size of 7 of the dimensions go to zero. It has 8 supersymmetries which is the most any gravitational theory can have since there are 8 half-steps between spin 2 and spin −2. (A graviton has the highest spin in this theory which is a spin 2 particle.) More supersymmetries would mean the particles would have superpartners with spins higher than 2. The only theories with spins higher than 2 which are consistent involve an infinite number of particles (such as string theory and higher-spin theories). <a href="/wiki/Stephen_Hawking" title="Stephen Hawking">Stephen Hawking</a> in his <i>A Brief History of Time</i> speculated that this theory could be the <a href="/wiki/Theory_of_Everything" class="mw-redirect" title="Theory of Everything">Theory of Everything</a>. However, in later years this was abandoned in favour of string theory. There has been renewed interest in the 21st century with the possibility that this theory may be finite. </p> <div class="mw-heading mw-heading2"><h2 id="Higher-dimensional_SUGRA">Higher-dimensional SUGRA</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Supergravity&action=edit&section=12" title="Edit section: Higher-dimensional SUGRA"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Higher-dimensional_supergravity" title="Higher-dimensional supergravity">Higher-dimensional supergravity</a></div> <p>Higher-dimensional SUGRA is the higher-dimensional, supersymmetric generalization of general relativity. Supergravity can be formulated in any number of dimensions up to eleven. Higher-dimensional SUGRA focuses upon supergravity in greater than four dimensions. </p><p>The number of supercharges in a <a href="/wiki/Spinor" title="Spinor">spinor</a> depends on the dimension and the signature of spacetime. The supercharges occur in spinors. Thus the limit on the number of supercharges cannot be satisfied in a spacetime of arbitrary dimension. Some theoretical examples in which this is satisfied are: </p> <ul><li>12-dimensional two-time theory</li> <li><a href="/wiki/Eleven-dimensional_supergravity" title="Eleven-dimensional supergravity">11-dimensional maximal supergravity</a></li> <li>10-dimensional supergravity theories <ul><li><a href="/wiki/Type_IIA_supergravity" title="Type IIA supergravity">Type IIA supergravity</a>: N = (1, 1)</li> <li><a href="/wiki/Type_IIB_supergravity" title="Type IIB supergravity">Type IIB supergravity</a>: N = (2, 0)</li> <li><a href="/wiki/Type_I_supergravity" title="Type I supergravity">Type I supergravity</a>: N = (1, 0)</li></ul></li> <li>9d supergravity theories <ul><li>Maximal 9d supergravity from 10d</li> <li>T-duality</li> <li>N = 1 Gauged supergravity</li></ul></li></ul> <p>The supergravity theories that have attracted the most interest contain no spins higher than two. This means, in particular, that they do not contain any fields that transform as symmetric tensors of rank higher than two under Lorentz transformations. The consistency of interacting higher spin field theories is, however, presently a field of very active interest. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Supergravity&action=edit&section=13" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 18em;"> <ul><li><a href="/wiki/General_relativity" title="General relativity">General relativity</a></li> <li><a href="/wiki/Grand_Unified_Theory" title="Grand Unified Theory">Grand Unified Theory</a></li> <li><a href="/wiki/M-theory" title="M-theory">M-theory</a></li> <li><a href="/wiki/N_%3D_8_supergravity" title="N = 8 supergravity"><i>N</i> = 8 supergravity</a></li> <li><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></li> <li><a href="/wiki/String_theory" title="String theory">String theory</a></li> <li><a href="/wiki/Supermanifold" title="Supermanifold">Supermanifold</a></li> <li><a href="/wiki/Super-Poincar%C3%A9_algebra" title="Super-Poincaré algebra">Super-Poincaré algebra</a></li> <li><a href="/wiki/Supersymmetry" title="Supersymmetry">Supersymmetry</a></li> <li><a href="/wiki/Supermetric" title="Supermetric">Supermetric</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Supergravity&action=edit&section=14" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output 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Vol. 18. pp. 529–533. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1973JETPL..18..312V">1973JETPL..18..312V</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBFb0105271">10.1007/BFb0105271</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-64623-5" title="Special:BookSources/978-3-540-64623-5"><bdi>978-3-540-64623-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Higgs+effect+for+goldstone+particles+with+spin+1%2F2&rft.btitle=Supersymmetry+and+Quantum+Field+Theory&rft.series=Lecture+Notes+in+Physics&rft.pages=529-533&rft.date=1973&rft_id=info%3Adoi%2F10.1007%2FBFb0105271&rft_id=info%3Abibcode%2F1973JETPL..18..312V&rft.isbn=978-3-540-64623-5&rft.aulast=Volkov&rft.aufirst=D.V.&rft.au=Soroka%2C+V.A&rft_id=http%3A%2F%2Fwww.jetpletters.ac.ru%2Fps%2F1568%2Farticle_24038.shtml&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASupergravity" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: </span><span class="cs1-visible-error citation-comment"><code class="cs1-code">|journal=</code> ignored (<a href="/wiki/Help:CS1_errors#periodical_ignored" title="Help:CS1 errors">help</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNathArnowitt1975" class="citation journal cs1">Nath, P.; Arnowitt, R. 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"Supergravity in theory in 11 dimensions". <i>Physics Letters B</i>. <b>76</b> (4): 409–412. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1978PhLB...76..409C">1978PhLB...76..409C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0370-2693%2878%2990894-8">10.1016/0370-2693(78)90894-8</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Letters+B&rft.atitle=Supergravity+in+theory+in+11+dimensions&rft.volume=76&rft.issue=4&rft.pages=409-412&rft.date=1978&rft_id=info%3Adoi%2F10.1016%2F0370-2693%2878%2990894-8&rft_id=info%3Abibcode%2F1978PhLB...76..409C&rft.aulast=Cremmer&rft.aufirst=E.&rft.au=Julia%2C+B.&rft.au=Scherk%2C+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASupergravity" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFreundRubin1980" class="citation journal cs1">Freund, P.; Rubin, M. (1980). "Dynamics of dimensional reduction". <i>Physics Letters B</i>. <b>97</b> (2): 233–235. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1980PhLB...97..233F">1980PhLB...97..233F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0370-2693%2880%2990590-0">10.1016/0370-2693(80)90590-0</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Letters+B&rft.atitle=Dynamics+of+dimensional+reduction&rft.volume=97&rft.issue=2&rft.pages=233-235&rft.date=1980&rft_id=info%3Adoi%2F10.1016%2F0370-2693%2880%2990590-0&rft_id=info%3Abibcode%2F1980PhLB...97..233F&rft.aulast=Freund&rft.aufirst=P.&rft.au=Rubin%2C+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASupergravity" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChamseddineArnowittNath1982" class="citation journal cs1">Chamseddine, A. H.; Arnowitt, R.; Nath, Pran (1982). "Locally supersymmetric grand unification". <i>Physical Review Letters</i>. <b>49</b> (14): 970–974. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1982PhRvL..49..970C">1982PhRvL..49..970C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.49.970">10.1103/PhysRevLett.49.970</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Locally+supersymmetric+grand+unification&rft.volume=49&rft.issue=14&rft.pages=970-974&rft.date=1982&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.49.970&rft_id=info%3Abibcode%2F1982PhRvL..49..970C&rft.aulast=Chamseddine&rft.aufirst=A.+H.&rft.au=Arnowitt%2C+R.&rft.au=Nath%2C+Pran&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASupergravity" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGreenSchwarz1984" class="citation journal cs1">Green, Michael B.; Schwarz, John H. (1984). "Anomaly cancellation in supersymmetric <i>D</i> = 10 gauge theory and superstring theory". <i>Physics Letters B</i>. <b>149</b> (1–3): 117–122. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1984PhLB..149..117G">1984PhLB..149..117G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0370-2693%2884%2991565-x">10.1016/0370-2693(84)91565-x</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Letters+B&rft.atitle=Anomaly+cancellation+in+supersymmetric+D+%3D+10+gauge+theory+and+superstring+theory&rft.volume=149&rft.issue=1%E2%80%933&rft.pages=117-122&rft.date=1984&rft_id=info%3Adoi%2F10.1016%2F0370-2693%2884%2991565-x&rft_id=info%3Abibcode%2F1984PhLB..149..117G&rft.aulast=Green&rft.aufirst=Michael+B.&rft.au=Schwarz%2C+John+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASupergravity" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDeser2018" class="citation journal cs1">Deser, S. (2018). <a rel="nofollow" class="external text" href="https://authors.library.caltech.edu/77015/1/1704.05886.pdf">"A brief history (and geography) of supergravity: The first 3 weeks... and after"</a> <span class="cs1-format">(PDF)</span>. <i>The European Physical Journal H</i>. <b>43</b> (3): 281–291. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1704.05886">1704.05886</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2018EPJH...43..281D">2018EPJH...43..281D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1140%2Fepjh%2Fe2018-90005-3">10.1140/epjh/e2018-90005-3</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:119428513">119428513</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+European+Physical+Journal+H&rft.atitle=A+brief+history+%28and+geography%29+of+supergravity%3A+The+first+3+weeks...+and+after&rft.volume=43&rft.issue=3&rft.pages=281-291&rft.date=2018&rft_id=info%3Aarxiv%2F1704.05886&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119428513%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1140%2Fepjh%2Fe2018-90005-3&rft_id=info%3Abibcode%2F2018EPJH...43..281D&rft.aulast=Deser&rft.aufirst=S.&rft_id=https%3A%2F%2Fauthors.library.caltech.edu%2F77015%2F1%2F1704.05886.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASupergravity" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDuplij2019" class="citation journal cs1">Duplij, S. (2019). <a rel="nofollow" class="external text" href="https://doi.org/10.26565%2F2312-4334-2019-3-10">"Supergravity was discovered by D.V. Volkov and V.A. Soroka in 1973, wasn't it?"</a>. <i>East European Journal of Physics</i> (3): 81–82. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1910.03259">1910.03259</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.26565%2F2312-4334-2019-3-10">10.26565/2312-4334-2019-3-10</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=East+European+Journal+of+Physics&rft.atitle=Supergravity+was+discovered+by+D.V.+Volkov+and+V.A.+Soroka+in+1973%2C+wasn%27t+it%3F&rft.issue=3&rft.pages=81-82&rft.date=2019&rft_id=info%3Aarxiv%2F1910.03259&rft_id=info%3Adoi%2F10.26565%2F2312-4334-2019-3-10&rft.aulast=Duplij&rft.aufirst=S.&rft_id=https%3A%2F%2Fdoi.org%2F10.26565%252F2312-4334-2019-3-10&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASupergravity" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading3"><h3 id="General">General</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Supergravity&action=edit&section=17" title="Edit section: General"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFde_Wit2002" class="citation arxiv cs1">de Wit, Bernard (2002). "Supergravity". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/hep-th/0212245">hep-th/0212245</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Supergravity&rft.date=2002&rft_id=info%3Aarxiv%2Fhep-th%2F0212245&rft.aulast=de+Wit&rft.aufirst=Bernard&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASupergravity" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPran2017" class="citation book cs1">Pran, Nath (2017). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=g7OSDQAAQBAJ"><i>Supersymmetry, Supergravity, and Unification</i></a>. <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-19702-1" title="Special:BookSources/978-0-521-19702-1"><bdi>978-0-521-19702-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Supersymmetry%2C+Supergravity%2C+and+Unification&rft.pub=Cambridge+University+Press&rft.date=2017&rft.isbn=978-0-521-19702-1&rft.aulast=Pran&rft.aufirst=Nath&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dg7OSDQAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASupergravity" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMartin1998" class="citation book cs1">Martin, Stephen P. (1998). "A Supersymmetry Primer". In Kane, Gordon L. (ed.). <i>Perspectives on Supersymmetry</i>. Advanced Series on Directions in High Energy Physics. Vol. 18. <a href="/wiki/World_Scientific" title="World Scientific">World Scientific</a>. pp. 1–98. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/hep-ph/9709356">hep-ph/9709356</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1142%2F9789812839657_0001">10.1142/9789812839657_0001</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-02-3553-6" title="Special:BookSources/978-981-02-3553-6"><bdi>978-981-02-3553-6</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:118973381">118973381</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=A+Supersymmetry+Primer&rft.btitle=Perspectives+on+Supersymmetry&rft.series=Advanced+Series+on+Directions+in+High+Energy+Physics&rft.pages=1-98&rft.pub=World+Scientific&rft.date=1998&rft_id=info%3Aarxiv%2Fhep-ph%2F9709356&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A118973381%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1142%2F9789812839657_0001&rft.isbn=978-981-02-3553-6&rft.aulast=Martin&rft.aufirst=Stephen+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASupergravity" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDreesGodboleRoy2004" class="citation book cs1">Drees, Manuel; Godbole, Rohini M.; Roy, Probir (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=U3jVCgAAQBAJ"><i>Theory and Phenomenology of Sparticles</i></a>. <a href="/wiki/World_Scientific" title="World Scientific">World Scientific</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9-810-23739-1" title="Special:BookSources/9-810-23739-1"><bdi>9-810-23739-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theory+and+Phenomenology+of+Sparticles&rft.pub=World+Scientific&rft.date=2004&rft.isbn=9-810-23739-1&rft.aulast=Drees&rft.aufirst=Manuel&rft.au=Godbole%2C+Rohini+M.&rft.au=Roy%2C+Probir&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DU3jVCgAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASupergravity" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBilal2001" class="citation arxiv cs1">Bilal, Adel (2001). "Introduction to Supersymmetry". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/hep-th/0101055">hep-th/0101055</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Introduction+to+Supersymmetry&rft.date=2001&rft_id=info%3Aarxiv%2Fhep-th%2F0101055&rft.aulast=Bilal&rft.aufirst=Adel&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASupergravity" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrandt2002" class="citation journal cs1">Brandt, Friedemann (2002). "Lectures on Supergravity". <i><a href="/wiki/Fortschritte_der_Physik" class="mw-redirect" title="Fortschritte der Physik">Fortschritte der Physik</a></i>. <b>50</b> (10–11): 1126–1172. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/hep-th/0204035">hep-th/0204035</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2002ForPh..50.1126B">2002ForPh..50.1126B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2F1521-3978%28200210%2950%3A10%2F11%3C1126%3A%3AAID-PROP1126%3E3.0.CO%3B2-B">10.1002/1521-3978(200210)50:10/11<1126::AID-PROP1126>3.0.CO;2-B</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:15471713">15471713</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Fortschritte+der+Physik&rft.atitle=Lectures+on+Supergravity&rft.volume=50&rft.issue=10%E2%80%9311&rft.pages=1126-1172&rft.date=2002&rft_id=info%3Aarxiv%2Fhep-th%2F0204035&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A15471713%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1002%2F1521-3978%28200210%2950%3A10%2F11%3C1126%3A%3AAID-PROP1126%3E3.0.CO%3B2-B&rft_id=info%3Abibcode%2F2002ForPh..50.1126B&rft.aulast=Brandt&rft.aufirst=Friedemann&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASupergravity" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSezgin2023" class="citation arxiv cs1">Sezgin, Ergin (2023). "Survey of supergravities". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2312.06754">2312.06754</a></span> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/hep-th">hep-th</a>].</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Survey+of+supergravities&rft.date=2023&rft_id=info%3Aarxiv%2F2312.06754&rft.aulast=Sezgin&rft.aufirst=Ergin&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASupergravity" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Supergravity&action=edit&section=18" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Dall'Agata, G., Zagermann, M., <i>Supergravity: From First Principles to Modern Applications</i>, Springer, (2021). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3662639788" title="Special:BookSources/978-3662639788">978-3662639788</a></li> <li>Freedman, D. Z., Van Proeyen, A., <i>Supergravity</i>, Cambridge University Press, Cambridge, (2012). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0521194013" title="Special:BookSources/978-0521194013">978-0521194013</a></li> <li>Lauria, E., Van Proeyen, A., <i>N = 2 Supergravity in D = 4, 5, 6 Dimensions</i>, Springer, (2020). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3030337551" title="Special:BookSources/978-3030337551">978-3030337551</a></li> <li>Nath, P., <i>Supersymmetry, Supergravity, and Unification</i>, Cambridge University Press, Cambridge, (2016) <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0521197021" title="Special:BookSources/978-0521197021">978-0521197021</a></li> <li>Tanii, Y., <i>Introduction to Supergravity</i>, Springer, (2014). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-4431548270" title="Special:BookSources/978-4431548270">978-4431548270</a></li> <li>Rausch de Traubenberg, M., Valenzuela, M., <i>A Supergravity Primer</i>, World Scientific Press, Singapore, (2019). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-9811210518" title="Special:BookSources/978-9811210518">978-9811210518</a></li> <li>Wess, P., <i>Introduction To Supersymmetry And Supergravity</i>, World Scientific Press, Singapore, (1990). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-9810200985" title="Special:BookSources/978-9810200985">978-9810200985</a></li> <li>Wess, P., Bagger, J., <i>Supersymmetry and Supergravity</i>, Princeton University Press, Princeton, (1992). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0691025308" title="Special:BookSources/978-0691025308">978-0691025308</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Supergravity&action=edit&section=19" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikiquote-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/13px-Wikiquote-logo.svg.png" decoding="async" width="13" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/20px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/27px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></a></span> Quotations related to <a href="https://en.wikiquote.org/wiki/Special:Search/Supergravity" class="extiw" title="wikiquote:Special:Search/Supergravity">Supergravity</a> at Wikiquote</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output 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.navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Supersymmetry" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="text-align:center;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Supersymmetry_topics" title="Template:Supersymmetry topics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Supersymmetry_topics" title="Template talk:Supersymmetry topics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Supersymmetry_topics" title="Special:EditPage/Template:Supersymmetry topics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Supersymmetry" style="font-size:114%;margin:0 4em"><a href="/wiki/Supersymmetry" title="Supersymmetry">Supersymmetry</a></div></th></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">General topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Supersymmetry" title="Supersymmetry">Supersymmetry</a></li> <li><a href="/wiki/Supersymmetric_gauge_theory" title="Supersymmetric gauge theory">Supersymmetric gauge theory</a></li> <li><a href="/wiki/Supersymmetric_quantum_mechanics" title="Supersymmetric quantum mechanics">Supersymmetric quantum mechanics</a></li> <li><a class="mw-selflink selflink">Supergravity</a></li> <li><a href="/wiki/Superstring_theory" title="Superstring theory">Superstring theory</a></li> <li><a href="/wiki/Super_vector_space" title="Super vector space">Super vector space</a></li> <li><a href="/wiki/Supergeometry" title="Supergeometry">Supergeometry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Supermathematics" title="Supermathematics">Supermathematics</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Superalgebra" title="Superalgebra">Superalgebra</a></li> <li><a href="/wiki/Lie_superalgebra" title="Lie superalgebra">Lie superalgebra</a></li> <li><a href="/wiki/Super-Poincar%C3%A9_algebra" title="Super-Poincaré algebra">Super-Poincaré algebra</a></li> <li><a href="/wiki/Superconformal_algebra" title="Superconformal algebra">Superconformal algebra</a></li> <li><a href="/wiki/Supersymmetry_algebra" title="Supersymmetry algebra">Supersymmetry algebra</a></li> <li><a href="/wiki/Supergroup_(physics)" title="Supergroup (physics)">Supergroup</a></li> <li><a href="/wiki/Superspace" title="Superspace">Superspace</a></li> <li><a href="/wiki/Harmonic_superspace" title="Harmonic superspace">Harmonic superspace</a></li> <li><a href="/wiki/Super_Minkowski_space" title="Super Minkowski space">Super Minkowski space</a></li> <li><a href="/wiki/Supermanifold" title="Supermanifold">Supermanifold</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Supercharge" title="Supercharge">Supercharge</a></li> <li><a href="/wiki/R-symmetry" title="R-symmetry">R-symmetry</a></li> <li><a href="/wiki/Supermultiplet" title="Supermultiplet">Supermultiplet</a></li> <li><a href="/wiki/Short_supermultiplet" title="Short supermultiplet">Short supermultiplet</a></li> <li><a href="/wiki/Bogomol%27nyi%E2%80%93Prasad%E2%80%93Sommerfield_state" title="Bogomol'nyi–Prasad–Sommerfield state">BPS state</a></li> <li><a href="/wiki/Superpotential" title="Superpotential">Superpotential</a></li> <li><a href="/wiki/D-term" title="D-term">D-term</a></li> <li><a href="/wiki/Fayet%E2%80%93Iliopoulos_D-term" title="Fayet–Iliopoulos D-term"> FI D-term</a></li> <li><a href="/wiki/F-term" title="F-term">F-term</a></li> <li><a href="/wiki/Moduli_(physics)" title="Moduli (physics)">Moduli space</a></li> <li><a href="/wiki/Supersymmetry_breaking" title="Supersymmetry breaking">Supersymmetry breaking</a></li> <li><a href="/wiki/Konishi_anomaly" title="Konishi anomaly">Konishi anomaly</a></li> <li><a href="/wiki/Seiberg_duality" title="Seiberg duality">Seiberg duality</a></li> <li><a href="/wiki/Seiberg%E2%80%93Witten_theory" title="Seiberg–Witten theory">Seiberg–Witten theory</a></li> <li><a href="/wiki/Witten_index" title="Witten index">Witten index</a></li> <li><a href="/wiki/Wess%E2%80%93Zumino_gauge" title="Wess–Zumino gauge">Wess–Zumino gauge</a></li> <li><a href="/wiki/Supersymmetric_localization" title="Supersymmetric localization">Localization</a></li> <li><a href="/wiki/Mu_problem" title="Mu problem">Mu problem</a></li> <li><a href="/wiki/Little_hierarchy_problem" title="Little hierarchy problem">Little hierarchy problem</a></li> <li><a href="/wiki/Montonen%E2%80%93Olive_duality" title="Montonen–Olive duality">Electric–magnetic duality</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Theorems</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Coleman%E2%80%93Mandula_theorem" title="Coleman–Mandula theorem">Coleman–Mandula</a></li> <li><a href="/wiki/Haag%E2%80%93%C5%81opusza%C5%84ski%E2%80%93Sohnius_theorem" title="Haag–Łopuszański–Sohnius theorem">Haag–Łopuszański–Sohnius</a></li> <li><a href="/wiki/Supersymmetry_nonrenormalization_theorems" title="Supersymmetry nonrenormalization theorems">Nonrenormalization</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Field theories</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Wess%E2%80%93Zumino_model" title="Wess–Zumino model">Wess–Zumino</a></li> <li><a href="/wiki/N_%3D_1_supersymmetric_Yang%E2%80%93Mills_theory" title="N = 1 supersymmetric Yang–Mills theory">N = 1 super Yang–Mills</a></li> <li><a href="/wiki/4D_N_%3D_1_global_supersymmetry" title="4D N = 1 global supersymmetry"> 4D N = 1</a></li> <li><a href="/wiki/N_%3D_4_supersymmetric_Yang%E2%80%93Mills_theory" title="N = 4 supersymmetric Yang–Mills theory">N = 4 super Yang–Mills</a></li> <li><a href="/wiki/Super_QCD" title="Super QCD">Super QCD</a></li> <li><a href="/wiki/Minimal_Supersymmetric_Standard_Model" title="Minimal Supersymmetric Standard Model">MSSM</a></li> <li><a href="/wiki/Next-to-Minimal_Supersymmetric_Standard_Model" title="Next-to-Minimal Supersymmetric Standard Model">NMSSM</a></li> <li><a href="/wiki/6D_(2,0)_superconformal_field_theory" title="6D (2,0) superconformal field theory">6D (2,0) superconformal</a></li> <li><a href="/wiki/ABJM_superconformal_field_theory" title="ABJM superconformal field theory">ABJM superconformal</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a class="mw-selflink selflink">Supergravity</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Pure_4D_N_%3D_1_supergravity" title="Pure 4D N = 1 supergravity">Pure 4D N = 1 supergravity</a></li> <li><a href="/wiki/4D_N_%3D_1_supergravity" title="4D N = 1 supergravity">4D N = 1 supergravity</a></li> <li><a href="/wiki/N_%3D_8_supergravity" title="N = 8 supergravity">N = 8 supergravity</a></li> <li><a href="/wiki/Higher_dimensional_supergravity" class="mw-redirect" title="Higher dimensional supergravity">Higher dimensional</a></li> <li><a href="/wiki/Eleven-dimensional_supergravity" title="Eleven-dimensional supergravity">11D supergravity</a></li> <li><a href="/wiki/Type_I_supergravity" title="Type I supergravity">Type I supergravity</a></li> <li><a href="/wiki/Type_IIA_supergravity" title="Type IIA supergravity">Type IIA supergravity</a></li> <li><a href="/wiki/Type_IIB_supergravity" title="Type IIB supergravity">Type IIB supergravity</a></li> <li><a href="/wiki/Gauged_supergravity" title="Gauged supergravity">Gauged supergravity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Superpartner" title="Superpartner">Superpartners</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Axino" title="Axino">Axino</a></li> <li><a href="/wiki/Chargino" title="Chargino">Chargino</a></li> <li><a href="/wiki/Gaugino" title="Gaugino">Gaugino</a></li> <li><a href="/wiki/Goldstino" title="Goldstino">Goldstino</a></li> <li><a href="/wiki/Graviphoton" title="Graviphoton">Graviphoton</a></li> <li><a href="/wiki/Graviscalar" title="Graviscalar">Graviscalar</a></li> <li><a href="/wiki/Higgsino" title="Higgsino">Higgsino</a></li> <li><a href="/wiki/Lightest_supersymmetric_particle" title="Lightest supersymmetric particle">LSP</a></li> <li><a href="/wiki/Neutralino" title="Neutralino">Neutralino</a></li> <li><a href="/wiki/R-hadron" title="R-hadron">R-hadron</a></li> <li><a href="/wiki/Sfermion" title="Sfermion">Sfermion</a></li> <li><a href="/wiki/Sgoldstino" title="Sgoldstino">Sgoldstino</a></li> <li><a href="/wiki/Stop_squark" title="Stop squark">Stop squark</a></li> <li><a href="/wiki/Superghost" title="Superghost">Superghost</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Researchers</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ian_Affleck" title="Ian Affleck">Affleck</a></li> <li><a href="/wiki/Jonathan_Bagger" title="Jonathan Bagger">Bagger</a></li> <li><a href="/wiki/Marjorie_Batchelor" title="Marjorie Batchelor">Batchelor</a></li> <li><a href="/wiki/Felix_Berezin" title="Felix Berezin">Berezin</a></li> <li><a href="/wiki/Michael_Dine" title="Michael Dine">Dine</a></li> <li><a href="/wiki/Pierre_Fayet" title="Pierre Fayet">Fayet</a></li> <li><a href="/wiki/Jim_Gates" class="mw-redirect" title="Jim Gates">Gates</a></li> <li><a href="/wiki/Yuri_Golfand" title="Yuri Golfand">Golfand</a></li> <li><a href="/wiki/John_Iliopoulos" title="John Iliopoulos">Iliopoulos</a></li> <li><a href="/wiki/Claus_Montonen" title="Claus Montonen">Montonen</a></li> <li><a href="/wiki/David_Olive" title="David Olive">Olive</a></li> <li><a href="/wiki/Abdus_Salam" title="Abdus Salam">Salam</a></li> <li><a href="/wiki/Nathan_Seiberg" title="Nathan Seiberg">Seiberg</a></li> <li><a href="/wiki/Warren_Siegel" title="Warren Siegel">Siegel</a></li> <li><a href="/wiki/Martin_Ro%C4%8Dek" title="Martin Roček">Roček</a></li> <li><a href="/wiki/Alice_Rogers" title="Alice Rogers">Rogers</a></li> <li><a href="/wiki/Julius_Wess" title="Julius Wess">Wess</a></li> <li><a href="/wiki/Edward_Witten" title="Edward Witten">Witten</a></li> <li><a href="/wiki/Bruno_Zumino" title="Bruno Zumino">Zumino</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="String_theory" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="text-align:center;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:String_theory_topics" title="Template:String theory topics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:String_theory_topics" title="Template talk:String theory topics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:String_theory_topics" title="Special:EditPage/Template:String theory topics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="String_theory" style="font-size:114%;margin:0 4em"><a href="/wiki/String_theory" title="String theory">String theory</a></div></th></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Background</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/String_(physics)" title="String (physics)">Strings</a></li> <li><a href="/wiki/Cosmic_string" title="Cosmic string">Cosmic strings</a></li> <li><a href="/wiki/History_of_string_theory" title="History of string theory">History of string theory</a> <ul><li><a href="/wiki/First_superstring_revolution" class="mw-redirect" title="First superstring revolution">First superstring revolution</a></li> <li><a href="/wiki/Second_superstring_revolution" class="mw-redirect" title="Second superstring revolution">Second superstring revolution</a></li></ul></li> <li><a href="/wiki/String_theory_landscape" title="String theory landscape">String theory landscape</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Theory</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nambu%E2%80%93Goto_action" title="Nambu–Goto action">Nambu–Goto action</a></li> <li><a href="/wiki/Polyakov_action" title="Polyakov action">Polyakov action</a></li> <li><a href="/wiki/Bosonic_string_theory" title="Bosonic string theory">Bosonic string theory</a></li> <li><a href="/wiki/Superstring_theory" title="Superstring theory">Superstring theory</a> <ul><li><a href="/wiki/Type_I_string_theory" title="Type I string theory">Type I string</a></li> <li><a href="/wiki/Type_II_string_theory" title="Type II string theory">Type II string</a> <ul><li><a href="/wiki/Type_II_string_theory" title="Type II string theory">Type IIA string</a></li> <li><a href="/wiki/Type_II_string_theory" title="Type II string theory">Type IIB string</a></li></ul></li> <li><a href="/wiki/Heterotic_string_theory" title="Heterotic string theory">Heterotic string</a></li></ul></li> <li><a href="/wiki/N%3D2_superstring" class="mw-redirect" title="N=2 superstring">N=2 superstring</a></li> <li><a href="/wiki/F-theory" title="F-theory">F-theory</a></li> <li><a href="/wiki/String_field_theory" title="String field theory">String field theory</a></li> <li><a href="/wiki/Matrix_string_theory" title="Matrix string theory">Matrix string theory</a></li> <li><a href="/wiki/Non-critical_string_theory" title="Non-critical string theory">Non-critical string theory</a></li> <li><a href="/wiki/Non-linear_sigma_model" title="Non-linear sigma model">Non-linear sigma model</a></li> <li><a href="/wiki/Tachyon_condensation" title="Tachyon condensation">Tachyon condensation</a></li> <li><a href="/wiki/RNS_formalism" title="RNS formalism">RNS formalism</a></li> <li><a href="/wiki/GS_formalism" title="GS formalism">GS formalism</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/String_duality" title="String duality">String duality</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/T-duality" title="T-duality">T-duality</a></li> <li><a href="/wiki/S-duality" title="S-duality">S-duality</a></li> <li><a href="/wiki/U-duality" title="U-duality">U-duality</a></li> <li><a href="/wiki/Montonen%E2%80%93Olive_duality" title="Montonen–Olive duality">Montonen–Olive duality</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Particles and fields</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Graviton" title="Graviton">Graviton</a></li> <li><a href="/wiki/Dilaton" title="Dilaton">Dilaton</a></li> <li><a href="/wiki/Tachyon" title="Tachyon">Tachyon</a></li> <li><a href="/wiki/Ramond%E2%80%93Ramond_field" title="Ramond–Ramond field">Ramond–Ramond field</a></li> <li><a href="/wiki/Kalb%E2%80%93Ramond_field" title="Kalb–Ramond field">Kalb–Ramond field</a></li> <li><a href="/wiki/Magnetic_monopole" title="Magnetic monopole">Magnetic monopole</a></li> <li><a href="/wiki/Dual_graviton" title="Dual graviton">Dual graviton</a></li> <li><a href="/wiki/Dual_photon" title="Dual photon">Dual photon</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Brane" title="Brane">Branes</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/D-brane" title="D-brane">D-brane</a></li> <li><a href="/wiki/NS5-brane" title="NS5-brane">NS5-brane</a></li> <li><a href="/wiki/M2-brane" title="M2-brane">M2-brane</a></li> <li><a href="/wiki/M5-brane" title="M5-brane">M5-brane</a></li> <li><a href="/wiki/S-brane" title="S-brane">S-brane</a></li> <li><a href="/wiki/Black_brane" title="Black brane">Black brane</a></li> <li><a href="/wiki/Black_hole" title="Black hole">Black holes</a></li> <li><a href="/wiki/Black_string" class="mw-redirect" title="Black string">Black string</a></li> <li><a href="/wiki/Brane_cosmology" title="Brane cosmology">Brane cosmology</a></li> <li><a href="/wiki/Quiver_diagram" title="Quiver diagram">Quiver diagram</a></li> <li><a href="/wiki/Hanany%E2%80%93Witten_transition" title="Hanany–Witten transition">Hanany–Witten transition</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Conformal_field_theory" title="Conformal field theory">Conformal field theory</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Virasoro_algebra" title="Virasoro algebra">Virasoro algebra</a></li> <li><a href="/wiki/Mirror_symmetry_(string_theory)" title="Mirror symmetry (string theory)">Mirror symmetry</a></li> <li><a href="/wiki/Conformal_anomaly" title="Conformal anomaly">Conformal anomaly</a></li> <li><a href="/wiki/Conformal_symmetry" title="Conformal symmetry">Conformal algebra</a></li> <li><a href="/wiki/Superconformal_algebra" title="Superconformal algebra">Superconformal algebra</a></li> <li><a href="/wiki/Vertex_operator_algebra" title="Vertex operator algebra">Vertex operator algebra</a></li> <li><a href="/wiki/Loop_algebra" title="Loop algebra">Loop algebra</a></li> <li><a href="/wiki/Kac%E2%80%93Moody_algebra" title="Kac–Moody algebra">Kac–Moody algebra</a></li> <li><a href="/wiki/Wess%E2%80%93Zumino%E2%80%93Witten_model" title="Wess–Zumino–Witten model">Wess–Zumino–Witten model</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Gauge_theory" title="Gauge theory">Gauge theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anomaly_(physics)" title="Anomaly (physics)">Anomalies</a></li> <li><a href="/wiki/Instanton" title="Instanton">Instantons</a></li> <li><a href="/wiki/Chern%E2%80%93Simons_form" title="Chern–Simons form">Chern–Simons form</a></li> <li><a href="/wiki/Bogomol%27nyi%E2%80%93Prasad%E2%80%93Sommerfield_bound" title="Bogomol'nyi–Prasad–Sommerfield bound">Bogomol'nyi–Prasad–Sommerfield bound</a></li> <li><a href="/wiki/Exceptional_Lie_group" class="mw-redirect" title="Exceptional Lie group">Exceptional Lie groups</a> (<a href="/wiki/G2_(mathematics)" title="G2 (mathematics)">G<sub>2</sub></a>, <a href="/wiki/F4_(mathematics)" title="F4 (mathematics)">F<sub>4</sub></a>, <a href="/wiki/E6_(mathematics)" title="E6 (mathematics)">E<sub>6</sub></a>, <a href="/wiki/E7_(mathematics)" title="E7 (mathematics)">E<sub>7</sub></a>, <a href="/wiki/E8_(mathematics)" title="E8 (mathematics)">E<sub>8</sub></a>)</li> <li><a href="/wiki/ADE_classification" title="ADE classification">ADE classification</a></li> <li><a href="/wiki/Dirac_string" title="Dirac string">Dirac string</a></li> <li><a href="/wiki/P-form_electrodynamics" title="P-form electrodynamics"><i>p</i>-form electrodynamics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Geometry</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Worldsheet" title="Worldsheet">Worldsheet</a></li> <li><a href="/wiki/Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein theory</a></li> <li><a href="/wiki/Compactification_(physics)" title="Compactification (physics)">Compactification</a></li> <li><a href="/wiki/Why_10_dimensions" class="mw-redirect" title="Why 10 dimensions">Why 10 dimensions</a>?</li> <li><a href="/wiki/K%C3%A4hler_manifold" title="Kähler manifold">Kähler manifold</a></li> <li><a href="/wiki/Ricci-flat_manifold" title="Ricci-flat manifold">Ricci-flat manifold</a> <ul><li><a href="/wiki/Calabi%E2%80%93Yau_manifold" title="Calabi–Yau manifold">Calabi–Yau manifold</a></li> <li><a href="/wiki/Hyperk%C3%A4hler_manifold" title="Hyperkähler manifold">Hyperkähler manifold</a> <ul><li><a href="/wiki/K3_surface" title="K3 surface">K3 surface</a></li></ul></li> <li><a href="/wiki/G2_manifold" title="G2 manifold">G<sub>2</sub> manifold</a></li> <li><a href="/wiki/Spin(7)-manifold" title="Spin(7)-manifold">Spin(7)-manifold</a></li></ul></li> <li><a href="/wiki/Generalized_complex_structure" title="Generalized complex structure">Generalized complex manifold</a></li> <li><a href="/wiki/Orbifold" title="Orbifold">Orbifold</a></li> <li><a href="/wiki/Conifold" title="Conifold">Conifold</a></li> <li><a href="/wiki/Orientifold" title="Orientifold">Orientifold</a></li> <li><a href="/wiki/Moduli_space" title="Moduli space">Moduli space</a></li> <li><a href="/wiki/Ho%C5%99ava%E2%80%93Witten_theory" title="Hořava–Witten theory">Hořava–Witten theory</a></li> <li><a href="/wiki/K-theory_(physics)" title="K-theory (physics)">K-theory (physics)</a></li> <li><a href="/wiki/Twisted_K-theory" title="Twisted K-theory">Twisted K-theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Supersymmetry" title="Supersymmetry">Supersymmetry</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Supergravity</a></li> <li><a href="/wiki/Eleven-dimensional_supergravity" title="Eleven-dimensional supergravity">Eleven-dimensional supergravity</a></li> <li><a href="/wiki/Type_I_supergravity" title="Type I supergravity">Type I supergravity</a></li> <li><a href="/wiki/Type_IIA_supergravity" title="Type IIA supergravity">Type IIA supergravity</a></li> <li><a href="/wiki/Type_IIB_supergravity" title="Type IIB supergravity">Type IIB supergravity</a></li> <li><a href="/wiki/Superspace" title="Superspace">Superspace</a></li> <li><a href="/wiki/Lie_superalgebra" title="Lie superalgebra">Lie superalgebra</a></li> <li><a href="/wiki/Lie_supergroup" class="mw-redirect" title="Lie supergroup">Lie supergroup</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Holography" title="Holography">Holography</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Holographic_principle" title="Holographic principle">Holographic principle</a></li> <li><a href="/wiki/AdS/CFT_correspondence" title="AdS/CFT correspondence">AdS/CFT correspondence</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/M-theory" title="M-theory">M-theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Matrix_theory_(physics)" title="Matrix theory (physics)">Matrix theory</a></li> <li><a href="/wiki/Introduction_to_M-theory" title="Introduction to M-theory">Introduction to M-theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">String theorists</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mina_Aganagi%C4%87" title="Mina Aganagić">Aganagić</a></li> <li><a href="/wiki/Nima_Arkani-Hamed" title="Nima Arkani-Hamed">Arkani-Hamed</a></li> <li><a href="/wiki/Michael_Atiyah" title="Michael Atiyah">Atiyah</a></li> <li><a href="/wiki/Tom_Banks_(physicist)" title="Tom Banks (physicist)">Banks</a></li> <li><a href="/wiki/David_Berenstein" title="David Berenstein">Berenstein</a></li> <li><a href="/wiki/Raphael_Bousso" title="Raphael Bousso">Bousso</a></li> <li><a href="/wiki/Thomas_Curtright" title="Thomas Curtright">Curtright</a></li> <li><a href="/wiki/Robbert_Dijkgraaf" title="Robbert Dijkgraaf">Dijkgraaf</a></li> <li><a href="/wiki/Jacques_Distler" title="Jacques Distler">Distler</a></li> <li><a href="/wiki/Michael_R._Douglas" title="Michael R. Douglas">Douglas</a></li> <li><a href="/wiki/Michael_Duff_(physicist)" title="Michael Duff (physicist)">Duff</a></li> <li><a href="/wiki/Gia_Dvali" class="mw-redirect" title="Gia Dvali">Dvali</a></li> <li><a href="/wiki/Sergio_Ferrara" title="Sergio Ferrara">Ferrara</a></li> <li><a href="/wiki/Willy_Fischler" title="Willy Fischler">Fischler</a></li> <li><a href="/wiki/Daniel_Friedan" title="Daniel Friedan">Friedan</a></li> <li><a href="/wiki/Sylvester_James_Gates" title="Sylvester James Gates">Gates</a></li> <li><a href="/wiki/Ferdinando_Gliozzi" title="Ferdinando Gliozzi">Gliozzi</a></li> <li><a href="/wiki/Rajesh_Gopakumar" title="Rajesh Gopakumar">Gopakumar</a></li> <li><a href="/wiki/Michael_Green_(physicist)" title="Michael Green (physicist)">Green</a></li> <li><a href="/wiki/Brian_Greene" title="Brian Greene">Greene</a></li> <li><a href="/wiki/David_Gross" title="David Gross">Gross</a></li> <li><a href="/wiki/Steven_Gubser" title="Steven Gubser">Gubser</a></li> <li><a href="/wiki/Sergei_Gukov" title="Sergei Gukov">Gukov</a></li> <li><a href="/wiki/Alan_Guth" title="Alan Guth">Guth</a></li> <li><a href="/wiki/Andrew_J._Hanson" title="Andrew J. Hanson">Hanson</a></li> <li><a href="/wiki/Jeffrey_A._Harvey" title="Jeffrey A. Harvey">Harvey</a></li> <li><a href="/wiki/Gerard_%27t_Hooft" title="Gerard 't Hooft">'t Hooft</a></li> <li><a href="/wiki/Petr_Ho%C5%99ava_(theorist)" class="mw-redirect" title="Petr Hořava (theorist)">Hořava</a></li> <li><a href="/wiki/Gary_Gibbons" title="Gary Gibbons">Gibbons</a></li> <li><a href="/wiki/Shamit_Kachru" title="Shamit Kachru">Kachru</a></li> <li><a href="/wiki/Michio_Kaku" title="Michio Kaku">Kaku</a></li> <li><a href="/wiki/Renata_Kallosh" title="Renata Kallosh">Kallosh</a></li> <li><a href="/wiki/Theodor_Kaluza" title="Theodor Kaluza">Kaluza</a></li> <li><a href="/wiki/Anton_Kapustin" title="Anton Kapustin">Kapustin</a></li> <li><a href="/wiki/Igor_Klebanov" title="Igor Klebanov">Klebanov</a></li> <li><a href="/wiki/Vadim_Knizhnik" title="Vadim Knizhnik">Knizhnik</a></li> <li><a href="/wiki/Maxim_Kontsevich" title="Maxim Kontsevich">Kontsevich</a></li> <li><a href="/wiki/Oskar_Klein" title="Oskar Klein">Klein</a></li> <li><a href="/wiki/Andrei_Linde" title="Andrei Linde">Linde</a></li> <li><a href="/wiki/Juan_Mart%C3%ADn_Maldacena" class="mw-redirect" title="Juan Martín Maldacena">Maldacena</a></li> <li><a href="/wiki/Stanley_Mandelstam" title="Stanley Mandelstam">Mandelstam</a></li> <li><a href="/wiki/Donald_Marolf" title="Donald Marolf">Marolf</a></li> <li><a href="/wiki/Emil_Martinec" title="Emil Martinec">Martinec</a></li> <li><a href="/wiki/Shiraz_Minwalla" title="Shiraz Minwalla">Minwalla</a></li> <li><a href="/wiki/Greg_Moore_(physicist)" title="Greg Moore (physicist)">Moore</a></li> <li><a href="/wiki/Lubo%C5%A1_Motl" title="Luboš Motl">Motl</a></li> <li><a href="/wiki/Sunil_Mukhi" title="Sunil Mukhi">Mukhi</a></li> <li><a href="/wiki/Robert_Myers_(physicist)" title="Robert Myers (physicist)">Myers</a></li> <li><a href="/wiki/Dimitri_Nanopoulos" title="Dimitri Nanopoulos">Nanopoulos</a></li> <li><a href="/wiki/Hora%C8%9Biu_N%C4%83stase" title="Horațiu Năstase">Năstase</a></li> <li><a href="/wiki/Nikita_Nekrasov" title="Nikita Nekrasov">Nekrasov</a></li> <li><a href="/wiki/Andr%C3%A9_Neveu" title="André Neveu">Neveu</a></li> <li><a href="/wiki/Holger_Bech_Nielsen" title="Holger Bech Nielsen">Nielsen</a></li> <li><a href="/wiki/Peter_van_Nieuwenhuizen" title="Peter van Nieuwenhuizen">van Nieuwenhuizen</a></li> <li><a href="/wiki/Sergei_Novikov_(mathematician)" title="Sergei Novikov (mathematician)">Novikov</a></li> <li><a href="/wiki/David_Olive" title="David Olive">Olive</a></li> <li><a href="/wiki/Hirosi_Ooguri" title="Hirosi Ooguri">Ooguri</a></li> <li><a href="/wiki/Burt_Ovrut" title="Burt Ovrut">Ovrut</a></li> <li><a href="/wiki/Joseph_Polchinski" title="Joseph Polchinski">Polchinski</a></li> <li><a href="/wiki/Alexander_Markovich_Polyakov" title="Alexander Markovich Polyakov">Polyakov</a></li> <li><a href="/wiki/Arvind_Rajaraman" title="Arvind Rajaraman">Rajaraman</a></li> <li><a href="/wiki/Pierre_Ramond" title="Pierre Ramond">Ramond</a></li> <li><a href="/wiki/Lisa_Randall" title="Lisa Randall">Randall</a></li> <li><a href="/wiki/Seifallah_Randjbar-Daemi" title="Seifallah Randjbar-Daemi">Randjbar-Daemi</a></li> <li><a href="/wiki/Martin_Ro%C4%8Dek" title="Martin Roček">Roček</a></li> <li><a href="/wiki/Ryan_Rohm" title="Ryan Rohm">Rohm</a></li> <li><a href="/wiki/Augusto_Sagnotti" title="Augusto Sagnotti">Sagnotti</a></li> <li><a href="/wiki/Jo%C3%ABl_Scherk" title="Joël Scherk">Scherk</a></li> <li><a href="/wiki/John_Henry_Schwarz" title="John Henry Schwarz">Schwarz</a></li> <li><a href="/wiki/Nathan_Seiberg" title="Nathan Seiberg">Seiberg</a></li> <li><a href="/wiki/Ashoke_Sen" title="Ashoke Sen">Sen</a></li> <li><a href="/wiki/Stephen_Shenker" title="Stephen Shenker">Shenker</a></li> <li><a href="/wiki/Warren_Siegel" title="Warren Siegel">Siegel</a></li> <li><a href="/wiki/Eva_Silverstein" title="Eva Silverstein">Silverstein</a></li> <li><a href="/wiki/%C4%90%C3%A0m_Thanh_S%C6%A1n" title="Đàm Thanh Sơn">Sơn</a></li> <li><a href="/wiki/Matthias_Staudacher" title="Matthias Staudacher">Staudacher</a></li> <li><a href="/wiki/Paul_Steinhardt" title="Paul Steinhardt">Steinhardt</a></li> <li><a href="/wiki/Andrew_Strominger" title="Andrew Strominger">Strominger</a></li> <li><a href="/wiki/Raman_Sundrum" title="Raman Sundrum">Sundrum</a></li> <li><a href="/wiki/Leonard_Susskind" title="Leonard Susskind">Susskind</a></li> <li><a href="/wiki/Paul_Townsend" title="Paul Townsend">Townsend</a></li> <li><a href="/wiki/Sandip_Trivedi" title="Sandip Trivedi">Trivedi</a></li> <li><a href="/wiki/Neil_Turok" title="Neil Turok">Turok</a></li> <li><a href="/wiki/Cumrun_Vafa" title="Cumrun Vafa">Vafa</a></li> <li><a href="/wiki/Gabriele_Veneziano" title="Gabriele Veneziano">Veneziano</a></li> <li><a href="/wiki/Erik_Verlinde" title="Erik Verlinde">Verlinde</a></li> <li><a href="/wiki/Herman_Verlinde" title="Herman Verlinde">Verlinde</a></li> <li><a href="/wiki/Julius_Wess" title="Julius Wess">Wess</a></li> <li><a href="/wiki/Edward_Witten" title="Edward Witten">Witten</a></li> <li><a href="/wiki/Shing-Tung_Yau" title="Shing-Tung Yau">Yau</a></li> <li><a href="/wiki/Tamiaki_Yoneya" title="Tamiaki Yoneya">Yoneya</a></li> <li><a href="/wiki/Alexander_Zamolodchikov" title="Alexander Zamolodchikov">Zamolodchikov</a></li> <li><a href="/wiki/Alexei_Zamolodchikov" title="Alexei Zamolodchikov">Zamolodchikov</a></li> <li><a href="/wiki/Eric_Zaslow" title="Eric Zaslow">Zaslow</a></li> <li><a href="/wiki/Bruno_Zumino" title="Bruno Zumino">Zumino</a></li> <li><a href="/wiki/Barton_Zwiebach" title="Barton Zwiebach">Zwiebach</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Theories_of_gravitation" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Theories_of_gravitation" title="Template:Theories of gravitation"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Theories_of_gravitation" title="Template talk:Theories of gravitation"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Theories_of_gravitation" title="Special:EditPage/Template:Theories of gravitation"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Theories_of_gravitation" style="font-size:114%;margin:0 4em"><a href="/wiki/Gravity" title="Gravity">Theories of gravitation</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Standard</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Newtonian gravity (NG)</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">Newton's law of universal gravitation</a></li> <li><a href="/wiki/Gauss%27s_law_for_gravity" title="Gauss's law for gravity">Gauss's law for gravity</a></li> <li><a href="/wiki/Poisson%27s_equation#Newtonian_gravity" title="Poisson's equation">Poisson's equation for gravity</a></li> <li><a href="/wiki/History_of_gravitational_theory" title="History of gravitational theory">History of gravitational theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/General_relativity" title="General relativity">General relativity (GR)</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Introduction_to_general_relativity" title="Introduction to general relativity">Introduction</a></li> <li><a href="/wiki/History_of_general_relativity" title="History of general relativity">History</a></li> <li><a href="/wiki/Mathematics_of_general_relativity" title="Mathematics of general relativity">Mathematics</a></li> <li><a href="/wiki/Exact_solutions_in_general_relativity" title="Exact solutions in general relativity">Exact solutions</a></li> <li><a href="/wiki/General_relativity#Further_reading" title="General relativity">Resources</a></li> <li><a href="/wiki/Tests_of_general_relativity" title="Tests of general relativity">Tests</a></li> <li><a href="/wiki/Parameterized_post-Newtonian_formalism" title="Parameterized post-Newtonian formalism">Post-Newtonian formalism</a></li> <li><a href="/wiki/Linearized_gravity" title="Linearized gravity">Linearized gravity</a></li> <li><a href="/wiki/ADM_formalism" title="ADM formalism">ADM formalism</a></li> <li><a href="/wiki/Gibbons%E2%80%93Hawking%E2%80%93York_boundary_term" title="Gibbons–Hawking–York boundary term">Gibbons–Hawking–York boundary term</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;line-height:1.2em;"><a href="/wiki/Alternatives_to_general_relativity" title="Alternatives to general relativity">Alternatives to<br />general relativity</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Paradigms</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alternatives_to_general_relativity" title="Alternatives to general relativity">Classical theories of gravitation</a></li> <li><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a></li> <li><a href="/wiki/Theory_of_everything" title="Theory of everything">Theory of everything</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Classical</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=Poincar%C3%A9_gauge_theory&action=edit&redlink=1" class="new" title="Poincaré gauge theory (page does not exist)">Poincaré gauge theory</a> <ul><li><span style="font-size:85%;"><a href="/wiki/Einstein%E2%80%93Cartan_theory" title="Einstein–Cartan theory">Einstein–Cartan</a></span></li> <li><span style="font-size:85%;"><a href="/wiki/Teleparallelism" title="Teleparallelism">Teleparallelism</a></span></li></ul></li> <li><a href="/wiki/Bimetric_gravity" title="Bimetric gravity">Bimetric theories</a></li> <li><a href="/wiki/Gauge_theory_gravity" title="Gauge theory gravity">Gauge theory gravity</a></li> <li><a href="/wiki/Composite_gravity" title="Composite gravity">Composite gravity</a></li> <li><a href="/wiki/F(R)_gravity" title="F(R) gravity"><i>f</i>(<i>R</i>) gravity</a></li> <li><a href="/wiki/Infinite_derivative_gravity" title="Infinite derivative gravity">Infinite derivative gravity</a></li> <li><a href="/wiki/Massive_gravity" title="Massive gravity">Massive gravity</a></li> <li><a href="/wiki/Modified_Newtonian_dynamics" title="Modified Newtonian dynamics">Modified Newtonian dynamics, MOND</a> <ul><li><span style="font-size:85%;"><a href="/wiki/AQUAL" title="AQUAL">AQUAL</a></span></li> <li><span style="font-size:85%;"><a href="/wiki/Tensor%E2%80%93vector%E2%80%93scalar_gravity" title="Tensor–vector–scalar gravity">Tensor–vector–scalar</a></span></li></ul></li> <li><a href="/wiki/Nonsymmetric_gravitational_theory" title="Nonsymmetric gravitational theory">Nonsymmetric gravitation</a></li> <li><a href="/wiki/Scalar%E2%80%93tensor_theory" title="Scalar–tensor theory">Scalar–tensor theories</a> <ul><li><span style="font-size:85%;"><a href="/wiki/Brans%E2%80%93Dicke_theory" title="Brans–Dicke theory">Brans–Dicke</a></span></li></ul></li> <li><a href="/wiki/Scalar%E2%80%93tensor%E2%80%93vector_gravity" title="Scalar–tensor–vector gravity">Scalar–tensor–vector</a></li> <li><a href="/wiki/Conformal_gravity" title="Conformal gravity">Conformal gravity</a></li> <li><a href="/wiki/Scalar_theories_of_gravitation" title="Scalar theories of gravitation">Scalar theories</a> <ul><li><span style="font-size:85%;"><a href="/wiki/Nordstr%C3%B6m%27s_theory_of_gravitation" title="Nordström's theory of gravitation">Nordström</a></span></li></ul></li> <li><a href="/wiki/Whitehead%27s_theory_of_gravitation" title="Whitehead's theory of gravitation">Whitehead</a></li> <li><a href="/wiki/Geometrodynamics" title="Geometrodynamics">Geometrodynamics</a></li> <li><a href="/wiki/Induced_gravity" title="Induced gravity">Induced gravity</a></li> <li><a href="/wiki/Degenerate_Higher-Order_Scalar-Tensor_theories" title="Degenerate Higher-Order Scalar-Tensor theories">Degenerate Higher-Order Scalar-Tensor theories</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Quantum-mechanical</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Euclidean_quantum_gravity" title="Euclidean quantum gravity">Euclidean quantum gravity</a></li> <li><a href="/wiki/Canonical_quantum_gravity" title="Canonical quantum gravity">Canonical quantum gravity</a> <ul><li><span style="font-size:85%;"><a href="/wiki/Wheeler%E2%80%93DeWitt_equation" title="Wheeler–DeWitt equation">Wheeler–DeWitt equation</a></span></li> <li><span style="font-size:85%;"><a href="/wiki/Loop_quantum_gravity" title="Loop quantum gravity">Loop quantum gravity</a></span></li> <li><span style="font-size:85%;"><a href="/wiki/Spin_foam" title="Spin foam">Spin foam</a></span></li></ul></li> <li><a href="/wiki/Causal_dynamical_triangulation" title="Causal dynamical triangulation">Causal dynamical triangulation</a></li> <li><a href="/wiki/Asymptotic_safety_in_quantum_gravity" title="Asymptotic safety in quantum gravity">Asymptotic safety in quantum gravity</a></li> <li><a href="/wiki/Causal_sets" title="Causal sets">Causal sets</a></li> <li><a href="/wiki/DGP_model" title="DGP model">DGP model</a></li> <li><a href="/wiki/Rainbow_gravity_theory" title="Rainbow gravity theory">Rainbow gravity theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Unified-field-theoric</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein theory</a></li> <li><a class="mw-selflink selflink">Supergravity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Unified-field-theoric and <br /> quantum-mechanical</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Noncommutative_quantum_field_theory" title="Noncommutative quantum field theory">Noncommutative geometry</a></li> <li><a href="/wiki/Semiclassical_gravity" title="Semiclassical gravity">Semiclassical gravity</a></li> <li><a href="/wiki/Superfluid_vacuum_theory" title="Superfluid vacuum theory">Superfluid vacuum theory</a> <ul><li><span style="font-size:85%;"><a href="/wiki/Superfluid_vacuum_theory#Logarithmic_BEC_vacuum_theory" title="Superfluid vacuum theory">Logarithmic BEC vacuum</a></span></li></ul></li> <li><a href="/wiki/String_theory" title="String theory">String theory</a> <ul><li><span style="font-size:85%;"><a href="/wiki/M-theory" title="M-theory">M-theory</a></span></li> <li><span style="font-size:85%;"><a href="/wiki/F-theory" title="F-theory">F-theory</a></span></li> <li><span style="font-size:85%;"><a href="/wiki/Heterotic_string_theory" title="Heterotic string theory">Heterotic string theory</a></span></li> <li><span style="font-size:85%;"><a href="/wiki/Type_I_string_theory" title="Type I string theory">Type I string theory</a></span></li> <li><span style="font-size:85%;"><a href="/wiki/Type_0_string_theory" title="Type 0 string theory">Type 0 string theory</a></span></li> <li><span style="font-size:85%;"><a href="/wiki/Bosonic_string_theory" title="Bosonic string theory">Bosonic string theory</a></span></li> <li><span style="font-size:85%;"><a href="/wiki/Type_II_string_theory" title="Type II string theory">Type II string theory</a></span></li> <li><span style="font-size:85%;"><a href="/wiki/Little_string_theory" title="Little string theory">Little string theory</a></span></li></ul></li> <li><a href="/wiki/Twistor_theory" title="Twistor theory">Twistor theory</a> <ul><li><span style="font-size:85%;"><a href="/wiki/Twistor_string_theory" title="Twistor string theory">Twistor string theory</a></span></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Generalisations / <br /> extensions of GR</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Liouville_gravity" class="mw-redirect" title="Liouville gravity">Liouville gravity</a></li> <li><a href="/wiki/Lovelock_theory_of_gravity" title="Lovelock theory of gravity">Lovelock theory</a></li> <li><a href="/wiki/(2%2B1)-dimensional_topological_gravity" title="(2+1)-dimensional topological gravity">(2+1)-dimensional topological gravity</a></li> <li><a href="/wiki/Gauss%E2%80%93Bonnet_gravity" title="Gauss–Bonnet gravity">Gauss–Bonnet gravity</a></li> <li><a href="/wiki/Jackiw%E2%80%93Teitelboim_gravity" title="Jackiw–Teitelboim gravity">Jackiw–Teitelboim gravity</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Pre-Newtonian<br />theories and<br /><a href="/wiki/Toy_model" title="Toy model">toy models</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aristotelian_physics" title="Aristotelian physics">Aristotelian physics</a></li> <li><a href="/wiki/CGHS_model" title="CGHS model">CGHS model</a></li> <li><a href="/wiki/RST_model" title="RST model">RST model</a></li> <li><a href="/wiki/Mechanical_explanations_of_gravitation" title="Mechanical explanations of gravitation">Mechanical explanations</a> <ul><li><span style="font-size:85%;"><a href="/wiki/Le_Sage%27s_theory_of_gravitation" title="Le Sage's theory of gravitation">Fatio–Le Sage</a></span></li> <li><span style="font-size:85%;"><a href="/wiki/Entropic_gravity" title="Entropic gravity">Entropic gravity</a></span></li></ul></li> <li><a href="/wiki/Gravitational_interaction_of_antimatter" title="Gravitational interaction of antimatter">Gravitational interaction of antimatter</a></li> <li><a href="/wiki/Physics_in_the_medieval_Islamic_world" title="Physics in the medieval Islamic world">Physics in the medieval Islamic world</a></li> <li><a href="/wiki/Theory_of_impetus" title="Theory of impetus">Theory of impetus</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Gravitational_wave" title="Gravitational wave">Gravitational wave</a></li> <li><a href="/wiki/Graviton" title="Graviton">Graviton</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Quantum_gravity" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Quantum_gravity" title="Template:Quantum gravity"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Quantum_gravity" title="Template talk:Quantum gravity"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Quantum_gravity" title="Special:EditPage/Template:Quantum gravity"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Quantum_gravity" style="font-size:114%;margin:0 4em"><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Central concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/AdS/CFT_correspondence" title="AdS/CFT correspondence">AdS/CFT correspondence</a></li> <li><a href="/wiki/Batalin%E2%80%93Vilkovisky_formalism" title="Batalin–Vilkovisky formalism">Batalin–Vilkovisky formalism</a></li> <li><a href="/wiki/CA-duality" title="CA-duality">CA-duality</a></li> <li><a href="/wiki/Causal_patch" title="Causal patch">Causal patch</a></li> <li><a href="/wiki/Faddeev%E2%80%93Popov_ghost" title="Faddeev–Popov ghost">Faddeev–Popov ghost</a></li> <li><a href="/wiki/Gravitational_anomaly" title="Gravitational anomaly">Gravitational anomaly</a></li> <li><a href="/wiki/Graviton" title="Graviton">Graviton</a></li> <li><a href="/wiki/Holographic_principle" title="Holographic principle">Holographic principle</a></li> <li><a href="/wiki/IR/UV_mixing" title="IR/UV mixing">IR/UV mixing</a></li> <li><a href="/wiki/Planck_units" title="Planck units">Planck units</a></li> <li><a href="/wiki/Quantum_foam" title="Quantum foam">Quantum foam</a></li> <li><a href="/wiki/Ryu%E2%80%93Takayanagi_conjecture" title="Ryu–Takayanagi conjecture">Ryu–Takayanagi conjecture</a></li> <li><a href="/wiki/Trans-Planckian_problem" title="Trans-Planckian problem">Trans-Planckian problem</a></li> <li><a href="/wiki/Weinberg%E2%80%93Witten_theorem" title="Weinberg–Witten theorem">Weinberg–Witten theorem</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Toy_model" title="Toy model">Toy models</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/(2%2B1)-dimensional_topological_gravity" title="(2+1)-dimensional topological gravity">2+1D topological gravity</a></li> <li><a href="/wiki/CGHS_model" title="CGHS model">CGHS model</a></li> <li><a href="/wiki/Jackiw%E2%80%93Teitelboim_gravity" title="Jackiw–Teitelboim gravity">Jackiw–Teitelboim gravity</a></li> <li><a href="/wiki/Liouville_gravity" class="mw-redirect" title="Liouville gravity">Liouville gravity</a></li> <li><a href="/wiki/RST_model" title="RST model">RST model</a></li> <li><a href="/wiki/Topological_quantum_field_theory" title="Topological quantum field theory">Topological quantum field theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_field_theory_in_curved_spacetime" title="Quantum field theory in curved spacetime">Quantum field theory<br />in curved spacetime</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bunch%E2%80%93Davies_vacuum" title="Bunch–Davies vacuum">Bunch–Davies vacuum</a></li> <li><a href="/wiki/Hawking_radiation" title="Hawking radiation">Hawking radiation</a></li> <li><a href="/wiki/Semiclassical_gravity" title="Semiclassical gravity">Semiclassical gravity</a></li> <li><a href="/wiki/Unruh_effect" title="Unruh effect">Unruh effect</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Black_hole" title="Black hole">Black holes</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Black_hole_complementarity" title="Black hole complementarity">Black hole complementarity</a></li> <li><a href="/wiki/Black_hole_information_paradox" title="Black hole information paradox">Black hole information paradox</a></li> <li><a href="/wiki/Black_hole_thermodynamics" title="Black hole thermodynamics">Black-hole thermodynamics</a></li> <li><a href="/wiki/Bekenstein_bound" title="Bekenstein bound">Bekenstein bound</a></li> <li><a href="/wiki/Bousso%27s_holographic_bound" title="Bousso's holographic bound">Bousso's holographic bound</a></li> <li><a href="/wiki/Cosmic_censorship_hypothesis" title="Cosmic censorship hypothesis">Cosmic censorship hypothesis</a></li> <li><a href="/wiki/ER_%3D_EPR" title="ER = EPR">ER = EPR</a></li> <li><a href="/wiki/Firewall_(physics)" title="Firewall (physics)">Firewall (physics)</a></li> <li><a href="/wiki/Gravitational_singularity" title="Gravitational singularity">Gravitational singularity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Approaches</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/String_theory" title="String theory">String theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bosonic_string_theory" title="Bosonic string theory">Bosonic string theory</a></li> <li><a href="/wiki/M-theory" title="M-theory">M-theory</a></li> <li><a class="mw-selflink selflink">Supergravity</a></li> <li><a href="/wiki/Superstring_theory" title="Superstring theory">Superstring theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Canonical_quantum_gravity" title="Canonical quantum gravity">Canonical quantum gravity</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Loop_quantum_gravity" title="Loop quantum gravity">Loop quantum gravity</a></li> <li><a href="/wiki/Wheeler%E2%80%93DeWitt_equation" title="Wheeler–DeWitt equation">Wheeler–DeWitt equation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Euclidean_quantum_gravity" title="Euclidean quantum gravity">Euclidean quantum gravity</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Hartle%E2%80%93Hawking_state" title="Hartle–Hawking state">Hartle–Hawking state</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Others</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Causal_dynamical_triangulation" title="Causal dynamical triangulation">Causal dynamical triangulation</a></li> <li><a href="/wiki/Causal_sets" title="Causal sets">Causal sets</a></li> <li><a href="/wiki/Dual_graviton" title="Dual graviton">Dual graviton</a></li> <li><a href="/wiki/Group_field_theory" title="Group field theory">Group field theory</a></li> <li><a href="/wiki/Noncommutative_geometry" title="Noncommutative geometry">Noncommutative geometry</a></li> <li><a href="/wiki/Spin_foam" title="Spin foam">Spin foam</a></li> <li><a href="/wiki/Superfluid_vacuum_theory" title="Superfluid vacuum theory">Superfluid vacuum theory</a></li> <li><a href="/wiki/Twistor_theory" title="Twistor theory">Twistor theory</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Applications</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_cosmology" title="Quantum cosmology">Quantum cosmology</a> <ul><li><a href="/wiki/Eternal_inflation" title="Eternal inflation">Eternal inflation</a></li> <li><a href="/wiki/FRW/CFT_duality" title="FRW/CFT duality">FRW/CFT duality</a></li> <li><a href="/wiki/Multiverse" title="Multiverse">Multiverse</a></li></ul></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><i>See also:</i> <span class="noviewer" typeof="mw:File"><span title="Template"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/16px-Symbol_template_class_pink.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/23px-Symbol_template_class_pink.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/31px-Symbol_template_class_pink.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Template:Quantum_mechanics_topics" title="Template:Quantum mechanics topics">Template:Quantum mechanics topics</a></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Standard_Model" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Standard_model_of_physics" title="Template:Standard model of physics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Standard_model_of_physics" title="Template talk:Standard model of physics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Standard_model_of_physics" title="Special:EditPage/Template:Standard model of physics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Standard_Model" style="font-size:114%;margin:0 4em"><a href="/wiki/Standard_Model" title="Standard Model">Standard Model</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Background</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Particle_physics" title="Particle physics">Particle physics</a> <ul><li><a href="/wiki/Fermion" title="Fermion">Fermions</a></li> <li><a href="/wiki/Gauge_boson" title="Gauge boson">Gauge boson</a></li> <li><a href="/wiki/Higgs_boson" title="Higgs boson">Higgs boson</a></li></ul></li> <li><a href="/wiki/Quantum_field_theory" title="Quantum field theory">Quantum field theory</a></li> <li><a href="/wiki/Gauge_theory" title="Gauge theory">Gauge theory</a></li> <li><a href="/wiki/Strong_interaction" title="Strong interaction">Strong interaction</a> <ul><li><a href="/wiki/Color_charge" title="Color charge">Color charge</a></li> <li><a href="/wiki/Quantum_chromodynamics" title="Quantum chromodynamics">Quantum chromodynamics</a></li> <li><a href="/wiki/Quark_model" title="Quark model">Quark model</a></li></ul></li> <li><a href="/wiki/Electroweak_interaction" title="Electroweak interaction">Electroweak interaction</a> <ul><li><a href="/wiki/Weak_interaction" title="Weak interaction">Weak interaction</a></li> <li><a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">Quantum electrodynamics</a></li> <li><a href="/wiki/Fermi%27s_interaction" title="Fermi's interaction">Fermi's interaction</a></li> <li><a href="/wiki/Weak_hypercharge" title="Weak hypercharge">Weak hypercharge</a></li> <li><a href="/wiki/Weak_isospin" title="Weak isospin">Weak isospin</a></li></ul></li></ul> </div></td><td class="noviewer navbox-image" rowspan="4" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Standard_Model_of_Elementary_Particles.svg/150px-Standard_Model_of_Elementary_Particles.svg.png" decoding="async" width="150" height="144" class="mw-file-element" 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title="Mathematical formulation of the Standard Model">Mathematical formulation of the Standard Model</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Physics_beyond_the_Standard_Model" title="Physics beyond the Standard Model">Beyond the<br />Standard Model</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Evidence</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Hierarchy_problem" title="Hierarchy problem">Hierarchy problem</a></li> <li><a href="/wiki/Dark_matter" title="Dark matter">Dark matter</a></li> <li><a href="/wiki/Cosmological_constant" title="Cosmological constant">Cosmological constant</a> <ul><li><a href="/wiki/Cosmological_constant_problem" title="Cosmological constant problem">problem</a></li></ul></li> <li><a href="/wiki/CP_violation" title="CP violation">Strong CP problem</a></li> <li><a href="/wiki/Neutrino_oscillation" title="Neutrino oscillation">Neutrino oscillation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theories</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Technicolor_(physics)" title="Technicolor (physics)">Technicolor</a></li> <li><a href="/wiki/Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein theory</a></li> <li><a href="/wiki/Grand_Unified_Theory" title="Grand Unified Theory">Grand Unified Theory</a></li> <li><a href="/wiki/Theory_of_everything" title="Theory of everything">Theory of everything</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Supersymmetry" title="Supersymmetry">Supersymmetry</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Minimal_Supersymmetric_Standard_Model" title="Minimal Supersymmetric Standard Model">MSSM</a></li> <li><a href="/wiki/Next-to-Minimal_Supersymmetric_Standard_Model" title="Next-to-Minimal Supersymmetric Standard Model">NMSSM</a></li> <li><a href="/wiki/Split_supersymmetry" title="Split supersymmetry">Split supersymmetry</a></li> <li><a class="mw-selflink selflink">Supergravity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/String_theory" title="String theory">String theory</a></li> <li><a href="/wiki/Superstring_theory" 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