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<span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Absence_of_physical_evidence" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Absence_of_physical_evidence"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Absence of physical evidence</span> </div> </a> <ul id="toc-Absence_of_physical_evidence-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Extra_dimensions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Extra_dimensions"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Extra dimensions</span> </div> </a> <ul id="toc-Extra_dimensions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Number_of_superstring_theories" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Number_of_superstring_theories"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Number of superstring theories</span> </div> </a> <ul id="toc-Number_of_superstring_theories-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Integrating_general_relativity_and_quantum_mechanics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Integrating_general_relativity_and_quantum_mechanics"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Integrating general relativity and quantum mechanics</span> </div> </a> <ul id="toc-Integrating_general_relativity_and_quantum_mechanics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mathematics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mathematics"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Mathematics</span> </div> </a> <button aria-controls="toc-Mathematics-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 Mathematics subsection</span> </button> <ul id="toc-Mathematics-sublist" class="vector-toc-list"> <li id="toc-D-branes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#D-branes"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>D-branes</span> </div> </a> <ul id="toc-D-branes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Why_five_superstring_theories?" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Why_five_superstring_theories?"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Why five superstring theories?</span> </div> </a> <ul id="toc-Why_five_superstring_theories?-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Beyond_superstring_theory" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Beyond_superstring_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Beyond superstring theory</span> </div> </a> <button aria-controls="toc-Beyond_superstring_theory-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 Beyond superstring theory subsection</span> </button> <ul id="toc-Beyond_superstring_theory-sublist" class="vector-toc-list"> <li id="toc-Compactification" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Compactification"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Compactification</span> </div> </a> <ul id="toc-Compactification-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kac–Moody_algebras" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kac–Moody_algebras"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Kac–Moody algebras</span> </div> </a> <ul id="toc-Kac–Moody_algebras-sublist" class="vector-toc-list"> </ul> </li> </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">9</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">10</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cited_sources" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cited_sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Cited sources</span> </div> </a> <ul id="toc-Cited_sources-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 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class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%B3%D9%88%D9%BE%D8%B1%D8%B3%DB%8C%D8%B2%DB%8C%D9%85_%D8%AA%D8%A6%D9%88%D8%B1%DB%8C%D8%B3%DB%8C" title="سوپرسیزیم تئوریسی – South Azerbaijani" lang="azb" hreflang="azb" data-title="سوپرسیزیم تئوریسی" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D1%81%D1%83%D0%BF%D0%B5%D1%80%D1%81%D1%82%D1%80%D1%83%D0%BD" title="Тэорыя суперструн – Belarusian" lang="be" hreflang="be" data-title="Тэорыя суперструн" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BD%D0%B0_%D1%81%D1%83%D0%BF%D0%B5%D1%80%D1%81%D1%82%D1%80%D1%83%D0%BD%D0%B8%D1%82%D0%B5" title="Теория на суперструните – Bulgarian" lang="bg" hreflang="bg" data-title="Теория на суперструните" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Teorie_superstrun" title="Teorie superstrun – Czech" lang="cs" hreflang="cs" data-title="Teorie superstrun" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Superstringiteooria" title="Superstringiteooria – Estonian" lang="et" hreflang="et" data-title="Superstringiteooria" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Teor%C3%ADa_de_supercuerdas" title="Teoría de supercuerdas – Spanish" lang="es" hreflang="es" data-title="Teoría de supercuerdas" 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/%D9%86%D8%B8%D8%B1%DB%8C%D9%87_%D8%A7%D8%A8%D8%B1%D8%B1%DB%8C%D8%B3%D9%85%D8%A7%D9%86" title="نظریه ابرریسمان – Persian" lang="fa" hreflang="fa" data-title="نظریه ابرریسمان" 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/Th%C3%A9orie_des_supercordes" title="Théorie des supercordes – French" lang="fr" hreflang="fr" data-title="Théorie des supercordes" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%B4%88%EB%81%88_%EC%9D%B4%EB%A1%A0" title="초끈 이론 – Korean" lang="ko" hreflang="ko" data-title="초끈 이론" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Teorio_di_superkordi" title="Teorio di superkordi – Ido" lang="io" hreflang="io" data-title="Teorio di superkordi" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Teori_adibenang" title="Teori adibenang – Indonesian" lang="id" hreflang="id" data-title="Teori adibenang" 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/Teoria_delle_superstringhe" title="Teoria delle superstringhe – Italian" lang="it" hreflang="it" data-title="Teoria delle superstringhe" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%AA%D7%95%D7%A8%D7%AA_%D7%94%D7%A2%D7%9C-%D7%9E%D7%99%D7%AA%D7%A8" title="תורת העל-מיתר – Hebrew" lang="he" hreflang="he" data-title="תורת העל-מיתר" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Superst%C4%ABgu_teorija" title="Superstīgu teorija – Latvian" lang="lv" hreflang="lv" data-title="Superstīgu teorija" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Superstyg%C5%B3_teorija" title="Superstygų teorija – Lithuanian" lang="lt" hreflang="lt" data-title="Superstygų teorija" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%98%D0%B0_%D0%BD%D0%B0_%D1%81%D1%83%D0%BF%D0%B5%D1%80%D1%81%D1%82%D1%80%D1%83%D0%BD%D0%B8%D1%82%D0%B5" title="Теорија на суперструните – Macedonian" lang="mk" hreflang="mk" data-title="Теорија на суперструните" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B8%E0%B5%82%E0%B4%AA%E0%B5%8D%E0%B4%AA%E0%B5%BC_%E0%B4%B8%E0%B5%8D%E0%B4%9F%E0%B5%8D%E0%B4%B0%E0%B4%BF%E0%B4%99%E0%B5%8D%E0%B4%99%E0%B5%8D_%E0%B4%B8%E0%B4%BF%E0%B4%A6%E0%B5%8D%E0%B4%A7%E0%B4%BE%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B4%82" title="സൂപ്പർ സ്ട്രിങ്ങ് സിദ്ധാന്തം – Malayalam" lang="ml" hreflang="ml" data-title="സൂപ്പർ സ്ട്രിങ്ങ് സിദ്ധാന്തം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%B6%85%E5%BC%A6%E7%90%86%E8%AB%96" title="超弦理論 – Japanese" lang="ja" hreflang="ja" data-title="超弦理論" 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-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Superstrengteori" title="Superstrengteori – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Superstrengteori" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Superstrengteori" title="Superstrengteori – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Superstrengteori" 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%B8%E0%A8%9F%E0%A8%B0%E0%A8%BF%E0%A9%B0%E0%A8%97_%E0%A8%A5%E0%A8%BF%E0%A8%8A%E0%A8%B0%E0%A9%80" title="ਸੁਪਰ-ਸਟਰਿੰਗ ਥਿਊਰੀ – Punjabi" lang="pa" hreflang="pa" data-title="ਸੁਪਰ-ਸਟਰਿੰਗ ਥਿਊਰੀ" 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/Teoria_superstrun" title="Teoria superstrun – Polish" lang="pl" hreflang="pl" data-title="Teoria superstrun" 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/Teoria_das_supercordas" title="Teoria das supercordas – Portuguese" lang="pt" hreflang="pt" data-title="Teoria das supercordas" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D1%81%D1%83%D0%BF%D0%B5%D1%80%D1%81%D1%82%D1%80%D1%83%D0%BD" title="Теория суперструн – Russian" lang="ru" hreflang="ru" data-title="Теория суперструн" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Superstring_theory" title="Superstring theory – Simple English" lang="en-simple" hreflang="en-simple" data-title="Superstring theory" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Teorija_superstrun" title="Teorija superstrun – Slovenian" lang="sl" hreflang="sl" data-title="Teorija superstrun" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Supers%C3%A4ieteoria" title="Supersäieteoria – Finnish" lang="fi" hreflang="fi" data-title="Supersäieteoria" 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/Superstr%C3%A4ngteori" title="Supersträngteori – Swedish" lang="sv" hreflang="sv" data-title="Supersträngteori" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/S%C3%BCpersicim_teorisi" title="Süpersicim teorisi – Turkish" lang="tr" hreflang="tr" data-title="Süpersicim teorisi" 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 href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D1%81%D1%83%D0%BF%D0%B5%D1%80%D1%81%D1%82%D1%80%D1%83%D0%BD" title="Теорія суперструн – Ukrainian" lang="uk" hreflang="uk" data-title="Теорія суперструн" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%B6%85%E5%BC%A6%E7%90%86%E8%AB%96" title="超弦理論 – Chinese" lang="zh" hreflang="zh" data-title="超弦理論" data-language-autonym="中文" data-language-local-name="Chinese" 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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 hlist"><tbody><tr><th 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 class="mw-selflink selflink">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 href="/wiki/Supergravity" title="Supergravity">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"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><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><b>Superstring theory</b> is an <a href="/wiki/Theory_of_everything" title="Theory of everything">attempt to explain all</a> of the <a href="/wiki/Elementary_particle" title="Elementary particle">particles</a> and <a href="/wiki/Fundamental_force" class="mw-redirect" title="Fundamental force">fundamental forces</a> of nature in one theory by modeling them as vibrations of tiny <a href="/wiki/Supersymmetry" title="Supersymmetry">supersymmetric</a> <a href="/wiki/String_(physics)" title="String (physics)">strings</a>. </p><p>'Superstring theory' is a shorthand for <b>supersymmetric string theory</b> because unlike <a href="/wiki/Bosonic_string_theory" title="Bosonic string theory">bosonic string theory</a>, it is the version of <a href="/wiki/String_theory" title="String theory">string theory</a> that accounts for both <a href="/wiki/Fermions" class="mw-redirect" title="Fermions">fermions</a> and <a href="/wiki/Bosons" class="mw-redirect" title="Bosons">bosons</a> and incorporates <a href="/wiki/Supersymmetry" title="Supersymmetry">supersymmetry</a> to model gravity. </p><p>Since the <a href="/wiki/Second_superstring_revolution" class="mw-redirect" title="Second superstring revolution">second superstring revolution</a>, the five superstring theories (<a href="/wiki/Type_I_string_theory" title="Type I string theory">Type I</a>, <a href="/wiki/Type_II_string_theory#Type_IIA_string_theory" title="Type II string theory">Type IIA</a>, <a href="/wiki/Type_II_string_theory#Type_IIB_string_theory" title="Type II string theory">Type IIB</a>, <a href="/wiki/Heterotic_string_theory" title="Heterotic string theory">HO and HE</a>) are regarded as different limits of a single theory tentatively called <a href="/wiki/M-theory" title="M-theory">M-theory</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Background">Background</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Superstring_theory&action=edit&section=1" title="Edit section: Background"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>One of the deepest open problems in <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physics</a> is formulating a theory of <a href="/wiki/Quantum_gravity" title="Quantum gravity">quantum gravity</a>. Such a theory incorporates both the theory of <a href="/wiki/General_relativity" title="General relativity">general relativity</a>, which describes gravitation and applies to large-scale structures, and <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> or more specifically <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a>, which describes the other three <a href="/wiki/Fundamental_forces" class="mw-redirect" title="Fundamental forces">fundamental forces</a> that act on the atomic scale. </p><p>Quantum field theory, in particular the <a href="/wiki/Standard_model" class="mw-redirect" title="Standard model">Standard model</a>, is currently the most successful theory to describe fundamental forces, but while computing physical quantities of interest, naïvely one obtains infinite values. Physicists developed the technique of <a href="/wiki/Renormalization" title="Renormalization">renormalization</a> to 'eliminate these infinities' to obtain finite values which can be experimentally tested. This technique works for three of the four fundamental forces: <a href="/wiki/Electromagnetism" title="Electromagnetism">Electromagnetism</a>, the <a href="/wiki/Strong_interaction" title="Strong interaction">strong force</a> and the <a href="/wiki/Weak_interaction" title="Weak interaction">weak</a> force, but does not work for <a href="/wiki/Gravity" title="Gravity">gravity</a>, which is non-renormalizable. Development of a <a href="/wiki/Quantum_theory_of_gravity" class="mw-redirect" title="Quantum theory of gravity">quantum theory of gravity</a> therefore requires different means than those used for the other forces.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>According to superstring theory, or more generally string theory, the fundamental constituents of reality are strings with radius on the order of the <a href="/wiki/Planck_units" title="Planck units">Planck length</a> (about 10<sup>−33</sup> cm). An appealing feature of string theory is that fundamental particles can be viewed as excitations of the string. The tension in a string is on the order of the <a href="/wiki/Planck_force" class="mw-redirect" title="Planck force">Planck force</a> (10<sup>44</sup> <a href="/wiki/Newton_(unit)" title="Newton (unit)">newtons</a>). The <a href="/wiki/Graviton" title="Graviton">graviton</a> (the proposed <a href="/wiki/Messenger_particle" class="mw-redirect" title="Messenger particle">messenger particle</a> of the gravitational force) is predicted by the theory to be a string with wave amplitude zero. </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=Superstring_theory&action=edit&section=2" title="Edit section: History"><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/History_of_string_theory" title="History of string theory">History of string theory</a></div> <p>Investigating how a string theory may include fermions in its spectrum led to the invention of <a href="/wiki/Supersymmetry" title="Supersymmetry">supersymmetry</a> (in <a href="/wiki/Western_world" title="Western world">the West</a><sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="Is this meant to hint at independendent work by non-western (who? where?) scientists? (November 2019)">clarification needed</span></a></i>]</sup>)<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> in 1971,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> a mathematical transformation between bosons and fermions. String theories that include fermionic vibrations are now known as "superstring theories". </p><p>Since its beginnings in the seventies and through the combined efforts of many different researchers, superstring theory has developed into a broad and varied subject with connections to <a href="/wiki/Quantum_gravity" title="Quantum gravity">quantum gravity</a>, <a href="/wiki/Particle_physics" title="Particle physics">particle</a> and <a href="/wiki/Condensed_matter_physics" title="Condensed matter physics">condensed matter physics</a>, <a href="/wiki/Cosmology" title="Cosmology">cosmology</a>, and <a href="/wiki/Pure_mathematics" title="Pure mathematics">pure mathematics</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Absence_of_physical_evidence">Absence of physical evidence</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Superstring_theory&action=edit&section=3" title="Edit section: Absence of physical evidence"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Superstring theory is based on supersymmetry. No supersymmetric particles have been discovered and initial investigation, carried out in 2011 at the <a href="/wiki/Large_Hadron_Collider" title="Large Hadron Collider">Large Hadron Collider</a> (LHC)<sup id="cite_ref-LHCinitSUSY_4-0" class="reference"><a href="#cite_note-LHCinitSUSY-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and in 2006 at the <a href="/wiki/Tevatron" title="Tevatron">Tevatron</a> has excluded some of the ranges.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability#Self-published_sources" title="Wikipedia:Verifiability"><span title="The material near this tag may rely on a self-published source. (July 2013)">self-published source?</span></a></i>]</sup><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><sup id="cite_ref-C4Wauto-5690134_7-0" class="reference"><a href="#cite_note-C4Wauto-5690134-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><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> For instance, the mass constraint of the <a href="/wiki/Minimal_Supersymmetric_Standard_Model" title="Minimal Supersymmetric Standard Model">Minimal Supersymmetric Standard Model</a> <a href="/wiki/Squark#Squarks" class="mw-redirect" title="Squark">squarks</a> has been up to 1.1 TeV, and <a href="/wiki/Gluinos" class="mw-redirect" title="Gluinos">gluinos</a> up to 500 GeV.<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> No report on suggesting <a href="/wiki/Large_extra_dimension" class="mw-redirect" title="Large extra dimension">large extra dimensions</a> has been delivered from the LHC. There have been no principles so far to limit the number of vacua in the concept of a landscape of vacua.<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> </p><p>Some particle physicists became disappointed by the lack of experimental verification of supersymmetry, and some have already discarded it.<sup id="cite_ref-Guardian-hit_buffers_11-0" class="reference"><a href="#cite_note-Guardian-hit_buffers-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Jon_Butterworth" title="Jon Butterworth">Jon Butterworth</a> at <a href="/wiki/University_College_London" title="University College London">University College London</a> said that we had no sign of supersymmetry, even in higher energy regions, excluding the <a href="/wiki/Superpartner" title="Superpartner">superpartners</a> of the top quark up to a few TeV. Ben Allanach at the University of Cambridge states that if we do not discover any new particles in the next trial at the LHC, then we can say it is unlikely to discover supersymmetry at <a href="/wiki/CERN" title="CERN">CERN</a> in the foreseeable future.<sup id="cite_ref-Guardian-hit_buffers_11-1" class="reference"><a href="#cite_note-Guardian-hit_buffers-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Extra_dimensions">Extra dimensions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Superstring_theory&action=edit&section=4" title="Edit section: Extra dimensions"><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">See also: <a href="/wiki/String_theory#Extra_dimensions" title="String theory">String theory § Extra dimensions</a></div> <p>Our <a href="/wiki/Physical_space" class="mw-redirect" title="Physical space">physical space</a> is observed to have <a href="/wiki/Three-dimensional_space" title="Three-dimensional space">three large spatial</a> <a href="/wiki/Dimension" title="Dimension">dimensions</a> and, along with <a href="/wiki/Time" title="Time">time</a>, is a boundless 4-dimensional <a href="/wiki/Continuum_(theory)" class="mw-redirect" title="Continuum (theory)">continuum</a> known as <a href="/wiki/Spacetime" title="Spacetime">spacetime</a>. However, nothing prevents a theory from including more than 4 dimensions. In the case of <a href="/wiki/String_theory" title="String theory">string theory</a>, <a href="/wiki/Consistency" title="Consistency">consistency</a> requires spacetime to have 10 dimensions (3D regular space + 1 time + 6D <a href="/wiki/Hyperspace" title="Hyperspace">hyperspace</a>).<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> The fact that we see only 3 dimensions of space can be explained by one of two mechanisms: either the extra dimensions are <a href="/wiki/Compactification_(physics)" title="Compactification (physics)">compactified</a> on a very small scale, or else our world may live on a 3-dimensional <a href="/wiki/Submanifold" title="Submanifold">submanifold</a> corresponding to a <a href="/wiki/Brane" title="Brane">brane</a>, on which all known particles besides gravity would be restricted. </p><p>If the extra dimensions are compactified, then the extra 6 dimensions must be in the form of a <a href="/wiki/Calabi%E2%80%93Yau_manifold" title="Calabi–Yau manifold">Calabi–Yau manifold</a>. Within the more complete framework of M-theory, they would have to take form of a <a href="/wiki/G2_manifold" title="G2 manifold">G2 manifold</a>. A particular exact symmetry of string/M-theory called <a href="/wiki/T-duality" title="T-duality">T-duality</a> (which exchanges momentum modes for <a href="/wiki/Winding_number" title="Winding number">winding number</a> and sends compact dimensions of radius R to radius 1/R),<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> has led to the discovery of equivalences between different Calabi–Yau manifolds called <a href="/wiki/Mirror_symmetry_(string_theory)" title="Mirror symmetry (string theory)">mirror symmetry</a>. </p><p>Superstring theory is not the first theory to propose extra spatial dimensions. It can be seen as building upon the <a href="/wiki/Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein theory</a>, which proposed a 4+1 dimensional (5D) theory of gravity. When compactified on a circle, the gravity in the extra dimension precisely describes <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a> from the perspective of the 3 remaining large space dimensions. Thus the original Kaluza–Klein theory is a prototype for the unification of gauge and gravity interactions, at least at the classical level, however it is known to be insufficient to describe nature for a variety of reasons (missing weak and strong forces, lack of <a href="/wiki/Parity_violation" class="mw-redirect" title="Parity violation">parity violation</a>, etc.) A more complex compact geometry is needed to reproduce the known gauge forces. Also, to obtain a consistent, fundamental, quantum theory requires the upgrade to string theory, not just the extra dimensions. </p> <div class="mw-heading mw-heading2"><h2 id="Number_of_superstring_theories">Number of superstring theories</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Superstring_theory&action=edit&section=5" title="Edit section: Number of superstring theories"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Theoretical physicists were troubled by the existence of five separate superstring theories. A possible solution for this dilemma was suggested at the beginning of what is called the <a href="/wiki/Second_superstring_revolution" class="mw-redirect" title="Second superstring revolution">second superstring revolution</a> in the 1990s, which suggests that the five string theories might be different limits of a single underlying theory, called M-theory. This remains a <a href="/wiki/Conjecture" title="Conjecture">conjecture</a>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable"> <tbody><tr style="background:#fff;"> <th colspan="8" class="dark">String theories </th></tr> <tr> <th class="dark">Type </th> <th class="dark"><a href="/wiki/N-dimensional_space" class="mw-redirect" title="N-dimensional space">Spacetime dimensions</a> </th> <th class="dark">SUSY generators </th> <th class="dark">chiral </th> <th class="dark">open strings </th> <th class="dark"><a href="/w/index.php?title=Heterotic_compactification&action=edit&redlink=1" class="new" title="Heterotic compactification (page does not exist)">heterotic compactification</a> </th> <th class="dark"><a href="/wiki/Gauge_group" class="mw-redirect" title="Gauge group">gauge group</a> </th> <th class="dark"><a href="/wiki/Tachyon" title="Tachyon">tachyon</a> </th></tr> <tr> <th style="background:#fcc;" class="dark">Bosonic (closed) </th> <td style="text-align:CENTER;" class="dark">26 </td> <td style="text-align:CENTER;" class="dark">N = 0 </td> <td style="text-align:CENTER;" class="dark">no </td> <td style="text-align:CENTER;" class="dark">no </td> <td style="text-align:CENTER;" class="dark">no </td> <td style="text-align:CENTER;" class="dark">none </td> <td style="background:#ffc;" class="dark">yes </td></tr> <tr> <th style="background:#fcc;" class="dark">Bosonic (open) </th> <td style="text-align:CENTER;" class="dark">26 </td> <td style="text-align:CENTER;" class="dark">N = 0 </td> <td style="text-align:CENTER;" class="dark">no </td> <td style="text-align:CENTER;" class="dark">yes </td> <td style="text-align:CENTER;" class="dark">no </td> <td style="text-align:CENTER;" class="dark">U(1) </td> <td style="background:#ffc;" class="dark">yes </td></tr> <tr> <th style="background:#fcc;" class="dark">I </th> <td style="text-align:CENTER;" class="dark">10 </td> <td style="text-align:CENTER;" class="dark">N = (1,0) </td> <td style="text-align:CENTER;" class="dark">yes </td> <td style="text-align:CENTER;" class="dark">yes </td> <td style="text-align:CENTER;" class="dark">no </td> <td style="text-align:CENTER;" class="dark">SO(32) </td> <td style="background:#ffc;" class="dark">no </td></tr> <tr> <th style="background:#fcc;" class="dark">IIA </th> <td style="text-align:CENTER;" class="dark">10 </td> <td style="text-align:CENTER;" class="dark">N = (1,1) </td> <td style="text-align:CENTER;" class="dark">no </td> <td style="text-align:CENTER;" class="dark">no </td> <td style="text-align:CENTER;" class="dark">no </td> <td style="text-align:CENTER;" class="dark">U(1) </td> <td style="background:#ffc;" class="dark">no </td></tr> <tr> <th style="background:#fcc;" class="dark">IIB </th> <td style="text-align:CENTER;" class="dark">10 </td> <td style="text-align:CENTER;" class="dark">N = (2,0) </td> <td style="text-align:CENTER;" class="dark">yes </td> <td style="text-align:CENTER;" class="dark">no </td> <td style="text-align:CENTER;" class="dark">no </td> <td style="text-align:CENTER;" class="dark">none </td> <td style="background:#ffc;" class="dark">no </td></tr> <tr> <th style="background:#fcc;" class="dark">HO </th> <td style="text-align:CENTER;" class="dark">10 </td> <td style="text-align:CENTER;" class="dark">N = (1,0) </td> <td style="text-align:CENTER;" class="dark">yes </td> <td style="text-align:CENTER;" class="dark">no </td> <td style="text-align:CENTER;" class="dark">yes </td> <td style="text-align:CENTER;" class="dark">SO(32) </td> <td style="background:#ffc;" class="dark">no </td></tr> <tr> <th style="background:#fcc;" class="dark">HE </th> <td style="text-align:CENTER;" class="dark">10 </td> <td style="text-align:CENTER;" class="dark">N = (1,0) </td> <td style="text-align:CENTER;" class="dark">yes </td> <td style="text-align:CENTER;" class="dark">no </td> <td style="text-align:CENTER;" class="dark">yes </td> <td style="text-align:CENTER;" class="dark">E<sub>8</sub> × E<sub>8</sub> </td> <td style="background:#ffc;" class="dark">no </td></tr> <tr> <th style="background:#fcc;" class="dark">M-theory </th> <td style="text-align:CENTER;" class="dark">11 </td> <td style="text-align:CENTER;" class="dark">N = 1 </td> <td style="text-align:CENTER;" class="dark">no </td> <td style="text-align:CENTER;" class="dark">no </td> <td style="text-align:CENTER;" class="dark">no </td> <td style="text-align:CENTER;" class="dark">none </td> <td style="background:#ffc;" class="dark">no </td></tr></tbody></table> <p>The five consistent superstring theories are: </p> <ul><li>The <a href="/wiki/Type_I_string" class="mw-redirect" title="Type I string">type I string</a> has one supersymmetry in the ten-dimensional sense (16 <a href="/wiki/Supercharge" title="Supercharge">supercharges</a>). This theory is special in the sense that it is based on unoriented <a href="/wiki/Closed_string" class="mw-redirect" title="Closed string">open</a> and <a href="/wiki/Closed_string" class="mw-redirect" title="Closed string">closed strings</a>, while the rest are based on oriented closed strings.</li> <li>The <a href="/wiki/Type_II_string" class="mw-redirect" title="Type II string">type II string</a> theories have two supersymmetries in the ten-dimensional sense (32 supercharges). There are actually two kinds of type II strings called type IIA and type IIB. They differ mainly in the fact that the IIA theory is non-<a href="/wiki/Chirality_(physics)" title="Chirality (physics)">chiral</a> (parity conserving) while the IIB theory is chiral (parity violating).</li> <li>The <a href="/wiki/Heterotic_string" class="mw-redirect" title="Heterotic string">heterotic string</a> theories are based on a peculiar hybrid of a type I superstring and a bosonic string. There are two kinds of heterotic strings differing in their ten-dimensional <a href="/wiki/Gauge_group" class="mw-redirect" title="Gauge group">gauge groups</a>: the heterotic <a href="/wiki/E8_(mathematics)" title="E8 (mathematics)"><i>E</i><sub>8</sub>×<i>E</i><sub>8</sub></a> string and the heterotic <a href="/wiki/Special_orthogonal_group" class="mw-redirect" title="Special orthogonal group">SO(32)</a> string. (The name heterotic SO(32) is slightly inaccurate since among the SO(32) <a href="/wiki/Lie_group" title="Lie group">Lie groups</a>, string theory singles out a quotient Spin(32)/Z<sub>2</sub> that is not equivalent to SO(32).)</li></ul> <p>Chiral <a href="/wiki/Gauge_theory" title="Gauge theory">gauge theories</a> can be inconsistent due to <a href="/wiki/Anomaly_(physics)" title="Anomaly (physics)">anomalies</a>. This happens when certain one-loop <a href="/wiki/Feynman_diagram" title="Feynman diagram">Feynman diagrams</a> cause a quantum mechanical breakdown of the gauge symmetry. The anomalies were canceled out via the <a href="/wiki/Green%E2%80%93Schwarz_mechanism" title="Green–Schwarz mechanism">Green–Schwarz mechanism</a>. </p><p>Even though there are only five superstring theories, making detailed predictions for real experiments requires information about exactly what physical configuration the theory is in. This considerably complicates efforts to test string theory because there is an astronomically high number—10<sup>500</sup> or more—of configurations that meet some of the basic requirements to be consistent with our world. Along with the extreme remoteness of the Planck scale, this is the other major reason it is hard to test superstring theory. </p><p>Another approach to the number of superstring theories refers to the <a href="/wiki/Mathematical_structure" title="Mathematical structure">mathematical structure</a> called <a href="/wiki/Composition_algebra" title="Composition algebra">composition algebra</a>. In the findings of <a href="/wiki/Abstract_algebra" title="Abstract algebra">abstract algebra</a> there are just seven composition algebras over the <a href="/wiki/Field_(mathematics)" title="Field (mathematics)">field</a> of <a href="/wiki/Real_number" title="Real number">real numbers</a>. In 1990 physicists R. Foot and G.C. Joshi in Australia stated that "the seven classical superstring theories are in one-to-one correspondence to the seven composition algebras".<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Integrating_general_relativity_and_quantum_mechanics">Integrating general relativity and quantum mechanics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Superstring_theory&action=edit&section=6" title="Edit section: Integrating general relativity and quantum mechanics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/General_relativity" title="General relativity">General relativity</a> typically deals with situations involving large mass objects in fairly large regions of <a href="/wiki/Spacetime" title="Spacetime">spacetime</a> whereas <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> is generally reserved for scenarios at the atomic scale (small spacetime regions). The two are very rarely used together, and the most common case that combines them is in the study of <a href="/wiki/Black_hole" title="Black hole">black holes</a>. Having <i>peak density</i>, or the maximum amount of matter possible in a space, and very small area, the two must be used in synchrony to predict conditions in such places. Yet, when used together, the equations fall apart, spitting out impossible answers, such as imaginary distances and less than one dimension. </p><p>The major problem with their incongruence is that, at <a href="/wiki/Planck_scale" class="mw-redirect" title="Planck scale">Planck scale</a> (a fundamental small unit of length) lengths, general relativity predicts a smooth, flowing surface, while quantum mechanics predicts a random, warped surface, which are nowhere near compatible. Superstring theory resolves this issue, replacing the classical idea of point particles with strings. These strings have an average diameter of the <a href="/wiki/Planck_length" class="mw-redirect" title="Planck length">Planck length</a>, with extremely small variances, which completely ignores the quantum mechanical predictions of Planck-scale length dimensional warping. Also, these surfaces can be mapped as branes. These branes can be viewed as objects with a morphism between them. In this case, the morphism will be the state of a string that stretches between brane A and brane B. </p><p><a href="/wiki/Gravitational_singularity" title="Gravitational singularity">Singularities</a> are avoided because the observed consequences of "<a href="/wiki/Big_Crunch" title="Big Crunch">Big Crunches</a>" never reach zero size. In fact, should the universe begin a "big crunch" sort of process, string theory dictates that the universe could never be smaller than the size of one string, at which point it would actually begin expanding. </p> <div class="mw-heading mw-heading2"><h2 id="Mathematics">Mathematics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Superstring_theory&action=edit&section=7" title="Edit section: Mathematics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="D-branes">D-branes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Superstring_theory&action=edit&section=8" title="Edit section: D-branes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>D-branes are membrane-like objects in 10D string theory. They can be thought of as occurring as a result of a <a href="/wiki/Kaluza%E2%80%93Klein" class="mw-redirect" title="Kaluza–Klein">Kaluza–Klein</a> compactification of 11D M-theory that contains membranes. Because compactification of a geometric theory produces extra <a href="/wiki/Vector_fields" class="mw-redirect" title="Vector fields">vector fields</a> the D-branes can be included in the action by adding an extra U(1) vector field to the string action. </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 \partial _{z}\rightarrow \partial _{z}+iA_{z}(z,{\overline {z}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo stretchy="false">→</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo>+</mo> <mi>i</mi> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>z</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>z</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial _{z}\rightarrow \partial _{z}+iA_{z}(z,{\overline {z}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1dcf8f328d802d53aae11563df8854170e3561ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.613ex; height:2.843ex;" alt="{\displaystyle \partial _{z}\rightarrow \partial _{z}+iA_{z}(z,{\overline {z}})}"></span></dd></dl> <p>In <b>type I</b> open string theory, the ends of open strings are always attached to D-brane surfaces. A string theory with more gauge fields such as SU(2) gauge fields would then correspond to the compactification of some higher-dimensional theory above 11 dimensions, which is not thought to be possible to date. Furthermore, the tachyons attached to the D-branes show the instability of those D-branes with respect to the annihilation. The tachyon total energy is (or reflects) the total energy of the D-branes. </p> <div class="mw-heading mw-heading3"><h3 id="Why_five_superstring_theories?"><span id="Why_five_superstring_theories.3F"></span>Why five superstring theories?</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Superstring_theory&action=edit&section=9" title="Edit section: Why five superstring theories?"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For a 10 dimensional supersymmetric theory we are allowed a 32-component Majorana spinor. This can be decomposed into a pair of 16-component Majorana-Weyl (chiral) <a href="/wiki/Spinors" class="mw-redirect" title="Spinors">spinors</a>. There are then various ways to construct an invariant depending on whether these two spinors have the same or opposite chiralities: </p> <table class="wikitable"> <tbody><tr> <th>Superstring model</th> <th>Invariant </th></tr> <tr> <td>Heterotic</td> <td><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 \partial _{z}X^{\mu }-i{\overline {\theta _{L}}}\Gamma ^{\mu }\partial _{z}\theta _{L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <mo>−</mo> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo accent="false">¯</mo> </mover> </mrow> <msup> <mi mathvariant="normal">Γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial _{z}X^{\mu }-i{\overline {\theta _{L}}}\Gamma ^{\mu }\partial _{z}\theta _{L}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b5796007be9aa1f81d2cd0c36cc7b25bca1450f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.01ex; height:3.343ex;" alt="{\displaystyle \partial _{z}X^{\mu }-i{\overline {\theta _{L}}}\Gamma ^{\mu }\partial _{z}\theta _{L}}"></span> </td></tr> <tr> <td>IIA</td> <td><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 \partial _{z}X^{\mu }-i{\overline {\theta _{L}}}\Gamma ^{\mu }\partial _{z}\theta _{L}-i{\overline {\theta _{R}}}\Gamma ^{\mu }\partial _{z}\theta _{R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <mo>−</mo> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo accent="false">¯</mo> </mover> </mrow> <msup> <mi mathvariant="normal">Γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>−</mo> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> <mo accent="false">¯</mo> </mover> </mrow> <msup> <mi mathvariant="normal">Γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial _{z}X^{\mu }-i{\overline {\theta _{L}}}\Gamma ^{\mu }\partial _{z}\theta _{L}-i{\overline {\theta _{R}}}\Gamma ^{\mu }\partial _{z}\theta _{R}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f754fafeee33a3da145f2f18743cbc176222411d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:32.821ex; height:3.343ex;" alt="{\displaystyle \partial _{z}X^{\mu }-i{\overline {\theta _{L}}}\Gamma ^{\mu }\partial _{z}\theta _{L}-i{\overline {\theta _{R}}}\Gamma ^{\mu }\partial _{z}\theta _{R}}"></span> </td></tr> <tr> <td>IIB</td> <td><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 \partial _{z}X^{\mu }-i{\overline {\theta _{L}^{1}}}\Gamma ^{\mu }\partial _{z}\theta _{L}^{1}-i{\overline {\theta _{L}^{2}}}\Gamma ^{\mu }\partial _{z}\theta _{L}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <mo>−</mo> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <msubsup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msubsup> <mo accent="false">¯</mo> </mover> </mrow> <msup> <mi mathvariant="normal">Γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <msubsup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msubsup> <mo>−</mo> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <msubsup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo accent="false">¯</mo> </mover> </mrow> <msup> <mi mathvariant="normal">Γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <msubsup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial _{z}X^{\mu }-i{\overline {\theta _{L}^{1}}}\Gamma ^{\mu }\partial _{z}\theta _{L}^{1}-i{\overline {\theta _{L}^{2}}}\Gamma ^{\mu }\partial _{z}\theta _{L}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc00ef80d107d95dcb742c9a158282b73a03aac9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:32.564ex; height:4.009ex;" alt="{\displaystyle \partial _{z}X^{\mu }-i{\overline {\theta _{L}^{1}}}\Gamma ^{\mu }\partial _{z}\theta _{L}^{1}-i{\overline {\theta _{L}^{2}}}\Gamma ^{\mu }\partial _{z}\theta _{L}^{2}}"></span> </td></tr></tbody></table> <p>The heterotic superstrings come in two types SO(32) and E<sub>8</sub>×E<sub>8</sub> as indicated above and the type I superstrings include open strings. </p> <div class="mw-heading mw-heading2"><h2 id="Beyond_superstring_theory">Beyond superstring theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Superstring_theory&action=edit&section=10" title="Edit section: Beyond superstring theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It is conceivable that the five superstring theories are approximated to a theory in higher dimensions possibly involving membranes. Because the action for this involves quartic terms and higher so is not <a href="/wiki/Gaussian" class="mw-redirect" title="Gaussian">Gaussian</a>, the functional integrals are very difficult to solve and so this has confounded the top theoretical physicists. <a href="/wiki/Edward_Witten" title="Edward Witten">Edward Witten</a> has popularised the concept of a theory in 11 dimensions, called M-theory, involving membranes interpolating from the known symmetries of superstring theory. It may turn out that there exist membrane models or other non-membrane models in higher dimensions—which may become acceptable when we find new unknown symmetries of nature, such as noncommutative geometry. It is thought, however, that 16 is probably the maximum since SO(16) is a maximal subgroup of E8, the largest exceptional Lie group, and also is more than large enough to contain the <a href="/wiki/Standard_Model" title="Standard Model">Standard Model</a>. Quartic integrals of the non-functional kind are easier to solve so there is hope for the future. This is the series solution, which is always convergent when a is non-zero and negative: </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 \int _{-\infty }^{\infty }\exp({ax^{4}+bx^{3}+cx^{2}+dx+f})\,dx=e^{f}\sum _{n,m,p=0}^{\infty }{\frac {b^{4n}}{(4n)!}}{\frac {c^{2m}}{(2m)!}}{\frac {d^{4p}}{(4p)!}}{\frac {\Gamma (3n+m+p+{\frac {1}{4}})}{a^{3n+m+p+{\frac {1}{4}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mi>exp</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>+</mo> <mi>b</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mi>c</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>d</mi> <mi>x</mi> <mo>+</mo> <mi>f</mi> </mrow> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msup> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>p</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> <mi>n</mi> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <mn>4</mn> <mi>n</mi> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>m</mi> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mi>m</mi> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> <mi>p</mi> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <mn>4</mn> <mi>p</mi> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mi>n</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mi>p</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <mo stretchy="false">)</mo> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mi>n</mi> <mo>+</mo> <mi>m</mi> <mo>+</mo> <mi>p</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{-\infty }^{\infty }\exp({ax^{4}+bx^{3}+cx^{2}+dx+f})\,dx=e^{f}\sum _{n,m,p=0}^{\infty }{\frac {b^{4n}}{(4n)!}}{\frac {c^{2m}}{(2m)!}}{\frac {d^{4p}}{(4p)!}}{\frac {\Gamma (3n+m+p+{\frac {1}{4}})}{a^{3n+m+p+{\frac {1}{4}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c76ace72ce64ff999b2ab73965d0e3d635d433b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:89.077ex; height:7.843ex;" alt="{\displaystyle \int _{-\infty }^{\infty }\exp({ax^{4}+bx^{3}+cx^{2}+dx+f})\,dx=e^{f}\sum _{n,m,p=0}^{\infty }{\frac {b^{4n}}{(4n)!}}{\frac {c^{2m}}{(2m)!}}{\frac {d^{4p}}{(4p)!}}{\frac {\Gamma (3n+m+p+{\frac {1}{4}})}{a^{3n+m+p+{\frac {1}{4}}}}}}"></span></dd></dl> <p>In the case of membranes the series would correspond to sums of various membrane interactions that are not seen in string theory. </p> <div class="mw-heading mw-heading3"><h3 id="Compactification">Compactification</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Superstring_theory&action=edit&section=11" title="Edit section: Compactification"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Investigating theories of higher dimensions often involves looking at the 10 dimensional superstring theory and interpreting some of the more obscure results in terms of compactified dimensions. For example, <a href="/wiki/D-branes" class="mw-redirect" title="D-branes">D-branes</a> are seen as compactified membranes from 11D M-theory. Theories of higher dimensions such as 12D F-theory and beyond produce other effects, such as gauge terms higher than U(1). The components of the extra vector fields (A) in the D-brane actions can be thought of as extra coordinates (X) in disguise. However, the <i>known</i> symmetries including <a href="/wiki/Supersymmetry" title="Supersymmetry">supersymmetry</a> currently restrict the <a href="/wiki/Spinors" class="mw-redirect" title="Spinors">spinors</a> to 32-components—which limits the number of dimensions to 11 (or 12 if you include two time dimensions.) Some physicists (e.g., <a href="/wiki/John_Baez" class="mw-redirect" title="John Baez">John Baez</a> et al.) have speculated that the exceptional <a href="/wiki/Lie_groups" class="mw-redirect" title="Lie groups">Lie groups</a> E<sub>6</sub>, E<sub>7</sub> and E<sub>8</sub> having maximum orthogonal subgroups SO(10), SO(12) and SO(16) may be related to theories in 10, 12 and 16 dimensions; 10 dimensions corresponding to string theory and the 12 and 16 dimensional theories being yet undiscovered but would be theories based on 3-branes and 7-branes respectively. However, this is a minority view within the string community. Since E<sub>7</sub> is in some sense F<sub>4</sub> quaternified and E<sub>8</sub> is F<sub>4</sub> octonified, the 12 and 16 dimensional theories, if they did exist, may involve the <a href="/wiki/Noncommutative_geometry" title="Noncommutative geometry">noncommutative geometry</a> based on the <a href="/wiki/Quaternions" class="mw-redirect" title="Quaternions">quaternions</a> and <a href="/wiki/Octonions" class="mw-redirect" title="Octonions">octonions</a> respectively. From the above discussion, it can be seen that physicists have many ideas for extending superstring theory beyond the current 10 dimensional theory, but so far all have been unsuccessful. </p> <div class="mw-heading mw-heading3"><h3 id="Kac–Moody_algebras"><span id="Kac.E2.80.93Moody_algebras"></span>Kac–Moody algebras</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Superstring_theory&action=edit&section=12" title="Edit section: Kac–Moody algebras"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Since strings can have an infinite number of modes, the symmetry used to describe string theory is based on infinite dimensional Lie algebras. Some <a href="/wiki/Kac%E2%80%93Moody_algebra" title="Kac–Moody algebra">Kac–Moody algebras</a> that have been considered as symmetries for M-theory have been E<sub>10</sub> and E<sub>11</sub> and their supersymmetric extensions. </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=Superstring_theory&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:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{clear:left;float:left;margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/25px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="25" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/37px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/49px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics portal</a></span></li></ul> <ul><li><a href="/wiki/AdS/CFT_correspondence" title="AdS/CFT correspondence">AdS/CFT correspondence</a></li> <li><a href="/wiki/DS/CFT_correspondence" title="DS/CFT correspondence">dS/CFT correspondence</a></li> <li><a href="/wiki/Grand_unification_theory" class="mw-redirect" title="Grand unification theory">Grand unification theory</a></li> <li><a href="/wiki/List_of_string_theory_topics" title="List of string theory topics">List of string theory topics</a></li> <li><a href="/wiki/String_field_theory" title="String field theory">String field theory</a></li></ul> <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=Superstring_theory&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 .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><a href="#CITEREFPolchinski1998a">Polchinski 1998a</a>, p. 4</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Rickles, Dean (2014). <i>A Brief History of String Theory: From Dual Models to M-Theory</i>. Springer, p. 104. <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-45128-7" title="Special:BookSources/978-3-642-45128-7">978-3-642-45128-7</a></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><a href="/wiki/Jean-Loup_Gervais" title="Jean-Loup Gervais">J. L. Gervais</a> and <a href="/wiki/Bunji_Sakita" title="Bunji Sakita">B. Sakita</a> worked on the two-dimensional case in which they use the concept of "supergauge," taken from Ramond, Neveu, and Schwarz's work on dual models: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGervaisSakita1971" class="citation journal cs1">Gervais, J.-L.; Sakita, B. (1971). 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CMS Collaboration: 221804. <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/1109.2352">1109.2352</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/2011PhRvL.107v1804C">2011PhRvL.107v1804C</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.107.221804">10.1103/PhysRevLett.107.221804</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0031-9007">0031-9007</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/22182023">22182023</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:22498269">22498269</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=Search+for+Supersymmetry+at+the+LHC+in+Events+with+Jets+and+Missing+Transverse+Energy&rft.volume=107&rft.issue=22&rft.pages=221804&rft.date=2011-11-21&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A22498269%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2011PhRvL.107v1804C&rft_id=info%3Aarxiv%2F1109.2352&rft.issn=0031-9007&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.107.221804&rft_id=info%3Apmid%2F22182023&rft.aulast=Chatrchyan&rft.aufirst=S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASuperstring+theory" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShifman2012" class="citation journal cs1">Shifman, M. (2012). "Frontiers Beyond the Standard Model: Reflections and Impressionistic Portrait of the Conference". <i>Modern Physics Letters A</i>. <b>27</b> (40): 1230043. <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/2012MPLA...2730043S">2012MPLA...2730043S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1142%2FS0217732312300431">10.1142/S0217732312300431</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Modern+Physics+Letters+A&rft.atitle=Frontiers+Beyond+the+Standard+Model%3A+Reflections+and+Impressionistic+Portrait+of+the+Conference&rft.volume=27&rft.issue=40&rft.pages=1230043&rft.date=2012&rft_id=info%3Adoi%2F10.1142%2FS0217732312300431&rft_id=info%3Abibcode%2F2012MPLA...2730043S&rft.aulast=Shifman&rft.aufirst=M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASuperstring+theory" class="Z3988"></span></span> </li> <li id="cite_note-Guardian-hit_buffers-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-Guardian-hit_buffers_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Guardian-hit_buffers_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJha2013" class="citation news cs1">Jha, Alok (August 6, 2013). <a rel="nofollow" class="external text" href="https://www.theguardian.com/science/2013/aug/06/higgs-boson-physics-hits-buffers-discovery">"One year on from the Higgs boson find, has physics hit the buffers?"</a>. <i><a href="/wiki/The_Guardian" title="The Guardian">The Guardian</a></i>. photograph: Harold Cunningham/Getty Images. <a href="/wiki/London,_England" class="mw-redirect" title="London, England">London</a>: <a href="/wiki/Guardian_Media_Group" title="Guardian Media Group">GMG</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0261-3077">0261-3077</a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/60623878">60623878</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140322225727/http://www.theguardian.com/science/2013/aug/06/higgs-boson-physics-hits-buffers-discovery">Archived</a> from the original on March 22, 2014<span class="reference-accessdate">. Retrieved <span class="nowrap">March 22,</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Guardian&rft.atitle=One+year+on+from+the+Higgs+boson+find%2C+has+physics+hit+the+buffers%3F&rft.date=2013-08-06&rft_id=info%3Aoclcnum%2F60623878&rft.issn=0261-3077&rft.aulast=Jha&rft.aufirst=Alok&rft_id=https%3A%2F%2Fwww.theguardian.com%2Fscience%2F2013%2Faug%2F06%2Fhiggs-boson-physics-hits-buffers-discovery&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASuperstring+theory" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">The <i>D</i> = 10 <a href="/wiki/Critical_dimension" title="Critical dimension">critical dimension</a> was originally discovered by <a href="/wiki/John_H._Schwarz" class="mw-redirect" title="John H. Schwarz">John H. Schwarz</a> in Schwarz, J. H. (1972). "Physical states and pomeron poles in the dual pion model". <i>Nuclear Physics</i>, <b>B46</b>(1), 61–74.</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><a href="#CITEREFPolchinski1998a">Polchinski 1998a</a>, p. 247</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><a href="#CITEREFPolchinski1998b">Polchinski 1998b</a>, p. 198</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFootJoshi1990" class="citation journal cs1">Foot, R.; Joshi, G. C. (1990). "Nonstandard signature of spacetime, superstrings, and the split composition algebras". <i>Letters in Mathematical Physics</i>. <b>19</b> (1): 65–71. <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/1990LMaPh..19...65F">1990LMaPh..19...65F</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%2FBF00402262">10.1007/BF00402262</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:120143992">120143992</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Letters+in+Mathematical+Physics&rft.atitle=Nonstandard+signature+of+spacetime%2C+superstrings%2C+and+the+split+composition+algebras&rft.volume=19&rft.issue=1&rft.pages=65-71&rft.date=1990&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120143992%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF00402262&rft_id=info%3Abibcode%2F1990LMaPh..19...65F&rft.aulast=Foot&rft.aufirst=R.&rft.au=Joshi%2C+G.+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASuperstring+theory" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Cited_sources">Cited sources</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Superstring_theory&action=edit&section=15" title="Edit section: Cited sources"><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="CITEREFPolchinski1998a" class="citation book cs1">Polchinski, Joseph (1998a). <i>String Theory Vol. 1: An Introduction to the Bosonic String</i>. <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/978-0-521-63303-1" title="Special:BookSources/978-0-521-63303-1"><bdi>978-0-521-63303-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=String+Theory+Vol.+1%3A+An+Introduction+to+the+Bosonic+String&rft.pub=Cambridge+University+Press&rft.date=1998&rft.isbn=978-0-521-63303-1&rft.aulast=Polchinski&rft.aufirst=Joseph&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASuperstring+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPolchinski1998b" class="citation book cs1">Polchinski, Joseph (1998b). <i>String Theory Vol. 2: Superstring Theory and Beyond</i>. <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/978-0-521-63304-8" title="Special:BookSources/978-0-521-63304-8"><bdi>978-0-521-63304-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=String+Theory+Vol.+2%3A+Superstring+Theory+and+Beyond&rft.pub=Cambridge+University+Press&rft.date=1998&rft.isbn=978-0-521-63304-8&rft.aulast=Polchinski&rft.aufirst=Joseph&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASuperstring+theory" class="Z3988"></span></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 .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .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 href="/wiki/Supergravity" title="Supergravity">Supergravity</a></li> <li><a class="mw-selflink selflink">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 href="/wiki/Supergravity" title="Supergravity">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 class="mw-selflink selflink">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 href="/wiki/Supergravity" title="Supergravity">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 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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="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" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Standard_Model_of_Elementary_Particles.svg/225px-Standard_Model_of_Elementary_Particles.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Standard_Model_of_Elementary_Particles.svg/300px-Standard_Model_of_Elementary_Particles.svg.png 2x" data-file-width="1390" data-file-height="1330" /></span></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Constituents</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/Cabibbo%E2%80%93Kobayashi%E2%80%93Maskawa_matrix" title="Cabibbo–Kobayashi–Maskawa matrix">CKM matrix</a></li> <li><a href="/wiki/Spontaneous_symmetry_breaking" title="Spontaneous symmetry breaking">Spontaneous symmetry breaking</a></li> <li><a href="/wiki/Higgs_mechanism" title="Higgs mechanism">Higgs mechanism</a></li> <li><a href="/wiki/Mathematical_formulation_of_the_Standard_Model" 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 href="/wiki/Supergravity" title="Supergravity">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 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