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</div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Alexander Markovich Polyakov</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 19 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-19" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">19 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A3%D9%84%D9%83%D8%B3%D9%86%D8%AF%D8%B1_%D9%85%D8%A7%D8%B1%D9%83%D9%88%D9%81%D9%8A%D8%AA%D8%B4_%D8%A8%D9%88%D9%84%D9%8A%D8%A7%D9%83%D9%88%D9%81" title="ألكسندر ماركوفيتش بولياكوف – Arabic" lang="ar" hreflang="ar" data-title="ألكسندر ماركوفيتش بولياكوف" data-language-autonym="العربية" data-language-local-name="Arabic" 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%A7%D9%84%DA%A9%D8%B3%D8%A7%D9%86%D8%AF%D8%B1_%D9%85%D8%A7%D8%B1%DA%A9%D9%88%D9%88%DB%8C%DA%86_%D9%BE%D9%88%D9%84%DB%8C%D8%A7%DA%A9%D9%88%D9%81" title="الکساندر مارکوویچ پولیاکوف – South Azerbaijani" lang="azb" hreflang="azb" data-title="الکساندر مارکوویچ پولیاکوف" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Alexandr_Poljakov" title="Alexandr Poljakov – Czech" lang="cs" hreflang="cs" data-title="Alexandr Poljakov" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Alexander_Markowitsch_Poljakow" title="Alexander Markowitsch Poljakow – German" lang="de" hreflang="de" data-title="Alexander Markowitsch Poljakow" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Aleksandr_Poliakov" title="Aleksandr Poliakov – Spanish" lang="es" hreflang="es" data-title="Aleksandr Poliakov" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D9%84%DA%A9%D8%B3%D8%A7%D9%86%D8%AF%D8%B1_%D9%85%D8%A7%D8%B1%DA%A9%D9%88%D9%88%DB%8C%DA%86_%D9%BE%D9%88%D9%84%DB%8C%D8%A7%DA%A9%D9%88%D9%81" title="الکساندر مارکوویچ پولیاکوف – Persian" lang="fa" hreflang="fa" data-title="الکساندر مارکوویچ پولیاکوف" 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/Alexander_Polyakov" title="Alexander Polyakov – French" lang="fr" hreflang="fr" data-title="Alexander Polyakov" 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%95%8C%EB%A0%89%EC%82%B0%EB%93%9C%EB%A5%B4_%EB%A7%88%EB%A5%B4%EC%BD%94%EB%B9%84%EC%B9%98_%ED%8F%B4%EB%9E%B4%EC%BD%94%ED%94%84" title="알렉산드르 마르코비치 폴랴코프 – Korean" lang="ko" hreflang="ko" data-title="알렉산드르 마르코비치 폴랴코프" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Aleksandr_Markovi%C4%8D_Poljakov" title="Aleksandr Markovič Poljakov – Italian" lang="it" hreflang="it" data-title="Aleksandr Markovič Poljakov" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Alexander_Polyakov" title="Alexander Polyakov – Haitian Creole" lang="ht" hreflang="ht" data-title="Alexander Polyakov" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%A7%D9%84%D9%83%D8%B3%D9%86%D8%AF%D8%B1_%D9%85%D8%A7%D8%B1%D9%83%D9%88%D9%81%D9%8A%D8%AA%D8%B4_%D8%A8%D9%88%D9%84%D9%8A%D8%A7%D9%83%D9%88%D9%81" title="الكسندر ماركوفيتش بولياكوف – Egyptian Arabic" lang="arz" hreflang="arz" data-title="الكسندر ماركوفيتش بولياكوف" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A2%E3%83%AC%E3%82%AF%E3%82%B5%E3%83%B3%E3%83%89%E3%83%AB%E3%83%BB%E3%83%9D%E3%83%AA%E3%83%A3%E3%82%B3%E3%83%95" title="アレクサンドル・ポリャコフ – Japanese" lang="ja" hreflang="ja" data-title="アレクサンドル・ポリャコフ" 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/Aleksandr_Poljakov" title="Aleksandr Poljakov – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Aleksandr Poljakov" 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-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Alexander_Polyakov" title="Alexander Polyakov – Portuguese" lang="pt" hreflang="pt" data-title="Alexander Polyakov" 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%9F%D0%BE%D0%BB%D1%8F%D0%BA%D0%BE%D0%B2,_%D0%90%D0%BB%D0%B5%D0%BA%D1%81%D0%B0%D0%BD%D0%B4%D1%80_%D0%9C%D0%B0%D1%80%D0%BA%D0%BE%D0%B2%D0%B8%D1%87" title="Поляков, Александр Маркович – Russian" lang="ru" hreflang="ru" data-title="Поляков, Александр Маркович" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Aleksander_Markovi%C4%8D_Poljakov" title="Aleksander Markovič Poljakov – Slovenian" lang="sl" hreflang="sl" data-title="Aleksander Markovič Poljakov" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Aleksandr_Poljakov" title="Aleksandr Poljakov – Swedish" lang="sv" hreflang="sv" data-title="Aleksandr Poljakov" 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/Aleksandr_Markovi%C3%A7_Polyakov" title="Aleksandr Markoviç Polyakov – Turkish" lang="tr" hreflang="tr" data-title="Aleksandr Markoviç Polyakov" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BA%9A%E5%8E%86%E5%B1%B1%E5%A4%A7%C2%B7%E9%A9%AC%E5%B0%94%E7%A7%91%E7%BB%B4%E5%A5%87%C2%B7%E6%B3%A2%E5%88%A9%E4%BA%9A%E7%A7%91%E5%A4%AB" title="亚历山大·马尔科维奇·波利亚科夫 – Chinese" lang="zh" hreflang="zh" data-title="亚历山大·马尔科维奇·波利亚科夫" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q277221#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul 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.infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Alexander M. Polyakov</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Polyakov_1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Polyakov_1.jpg/220px-Polyakov_1.jpg" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Polyakov_1.jpg/330px-Polyakov_1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Polyakov_1.jpg/440px-Polyakov_1.jpg 2x" data-file-width="1350" data-file-height="1350" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span style="display:none"> (<span class="bday">1945-09-27</span>) </span>27 September 1945<span class="noprint ForceAgeToShow"> (age 79)</span><br /><div style="display:inline" class="birthplace"><a href="/wiki/Moscow" title="Moscow">Moscow</a>, <a href="/wiki/Russian_SFSR" class="mw-redirect" title="Russian SFSR">Russian SFSR</a>, <a href="/wiki/Soviet_Union" title="Soviet Union">Soviet Union</a></div></td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/Moscow_Institute_of_Physics_and_Technology" title="Moscow Institute of Physics and Technology">Moscow Institute of Physics and Technology</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><a href="/wiki/%27t_Hooft%E2%80%93Polyakov_monopole" title="'t Hooft–Polyakov monopole">'t Hooft–Polyakov monopole</a><br /><a href="/wiki/BPST_instanton" title="BPST instanton">BPST instanton</a><br /><a href="/wiki/Polyakov_action" title="Polyakov action">Polyakov action</a><br /><a href="/wiki/Conformal_bootstrap" title="Conformal bootstrap">Conformal bootstrap</a><br /><a href="/wiki/Belavin%E2%80%93Polyakov%E2%80%93Zamolodchikov_equations" class="mw-redirect" title="Belavin–Polyakov–Zamolodchikov equations">Belavin–Polyakov–Zamolodchikov equations</a><br /><a href="/wiki/Liouville_field_theory" title="Liouville field theory">Liouville field theory</a><br /><a href="/wiki/AdS/CFT_correspondence" title="AdS/CFT correspondence">AdS/CFT correspondence</a><br /><a href="/wiki/Polyakov_loop" title="Polyakov loop">Polyakov loop</a><br /><a href="/wiki/Higgs_mechanism" title="Higgs mechanism">Higgs mechanism</a><br /><a href="/wiki/Higher-spin_theory" title="Higher-spin theory">Higher-spin theory</a><br /><a href="/wiki/Polyakov_formula" title="Polyakov formula">Polyakov formula</a></td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data"><span class="nowrap"><a href="/wiki/Max_Planck_Medal" title="Max Planck Medal">Max Planck Medal</a> (2021)<br /><a href="/wiki/Breakthrough_Prize_in_Fundamental_Physics" title="Breakthrough Prize in Fundamental Physics">Breakthrough Prize in Fundamental Physics</a> (2013)<br /><a href="/wiki/Lars_Onsager_Prize" title="Lars Onsager Prize">Lars Onsager Prize</a> (2011)<br /><a href="/wiki/Harvey_Prize" title="Harvey Prize">Harvey Prize</a> (2010)<br /><a href="/wiki/Pomeranchuk_Prize" title="Pomeranchuk Prize">Pomeranchuk Prize</a> (2004)<br /><a href="/wiki/Oskar_Klein_Memorial_Lecture" title="Oskar Klein Memorial Lecture">Oskar Klein Medal</a> (1996)<br /><a href="/wiki/Lorentz_Medal" title="Lorentz Medal">Lorentz Medal</a> (1994)<br /><a href="/wiki/Dannie_Heineman_Prize_for_Mathematical_Physics" title="Dannie Heineman Prize for Mathematical Physics">Dannie Heineman Prize</a> (1986)<br /><a href="/wiki/Dirac_Medal_(ICTP)" title="Dirac Medal (ICTP)">Dirac Medal of the ICTP</a> (1986)</span></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Theoretical_Physics" class="mw-redirect" title="Theoretical Physics">Theoretical</a> <a href="/wiki/High_energy_physics" class="mw-redirect" title="High energy physics">high energy physics</a></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><a href="/wiki/Princeton_University" title="Princeton University">Princeton University</a><br /><a href="/wiki/Landau_Institute_for_Theoretical_Physics" title="Landau Institute for Theoretical Physics">Landau Institute for Theoretical Physics</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Doctoral_advisor" title="Doctoral advisor">Doctoral advisor</a></th><td class="infobox-data"><a href="/wiki/Karen_Ter-Martirosian" title="Karen Ter-Martirosian">Karen Ter-Martirosian</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><b>Alexander Markovich Polyakov</b> (<a href="/wiki/Russian_language" title="Russian language">Russian</a>: <span lang="ru">Алекса́ндр Ма́ркович Поляко́в</span>; born 27 September 1945) is a Russian theoretical <a href="/wiki/Physicist" title="Physicist">physicist</a>, formerly at the <a href="/wiki/Landau_Institute_for_Theoretical_Physics" title="Landau Institute for Theoretical Physics">Landau Institute</a> in Moscow and, since 1989, at <a href="/wiki/Princeton_University" title="Princeton University">Princeton University</a>, where he is the <a href="/wiki/Joseph_Henry" title="Joseph Henry">Joseph Henry</a> Professor of Physics Emeritus.<sup id="cite_ref-c_1-0" class="reference"><a href="#cite_note-c-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></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> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Important_discoveries">Important discoveries</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alexander_Markovich_Polyakov&action=edit&section=1" title="Edit section: Important discoveries"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Polyakov is known for a number of fundamental contributions to <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a>, including work on what is now called the <a href="/wiki/%27t_Hooft%E2%80%93Polyakov_monopole" title="'t Hooft–Polyakov monopole">'t Hooft–Polyakov monopole</a> in <a href="/wiki/Non-abelian_gauge_theory" class="mw-redirect" title="Non-abelian gauge theory">non-Abelian gauge theory</a>, independent from <a href="/wiki/Gerard_%27t_Hooft" title="Gerard 't Hooft">Gerard 't Hooft</a>. Polyakov and coauthors discovered the so-called <a href="/wiki/BPST_instanton" title="BPST instanton">BPST instanton</a> which, in turn, led to the discovery of the <a href="/wiki/Theta_vacuum" title="Theta vacuum">vacuum angle</a> in <a href="/wiki/Quantum_chromodynamics" title="Quantum chromodynamics">QCD</a>.<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><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> His <a href="/wiki/Path_integral_formulation" title="Path integral formulation">path integral formulation</a> of <a href="/wiki/String_theory" title="String theory">string theory</a><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> had profound and lasting impacts on the conceptual and mathematical understanding of the theory. His paper "Infinite conformal symmetry in two-dimensional quantum field theory"<sup id="cite_ref-a_6-0" class="reference"><a href="#cite_note-a-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> written with <a href="/wiki/Alexander_Belavin" title="Alexander Belavin">Alexander Belavin</a> and <a href="/wiki/Alexander_Zamolodchikov" title="Alexander Zamolodchikov">Alexander Zamolodchikov</a> laid down the foundations of <a href="/wiki/Two-dimensional_conformal_field_theory" title="Two-dimensional conformal field theory">two-dimensional conformal field theory</a> and has classic status.<sup id="cite_ref-c_1-1" class="reference"><a href="#cite_note-c-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Polyakov also played an important role in elucidating the conceptual framework behind <a href="/wiki/Renormalization" title="Renormalization">renormalization</a> independent of <a href="/wiki/Kenneth_G._Wilson" title="Kenneth G. Wilson">Kenneth G. Wilson</a>'s Nobel Prize–winning work. He formulated pioneering ideas in gauge/string duality long before the breakthrough of <a href="/wiki/AdS/CFT" class="mw-redirect" title="AdS/CFT">AdS/CFT</a> using <a href="/wiki/D-branes" class="mw-redirect" title="D-branes">D-branes</a>. Other insightful conjectures that came years or even decades before active work by others include integrability of gauge and string theories and certain ideas about turbulence. </p><p>Very early in his career, in a 1965 student work, Polyakov suggested (with <a href="/wiki/Alexander_Arkadyevich_Migdal" title="Alexander Arkadyevich Migdal">Alexander Migdal</a>) a dynamical <a href="/wiki/Higgs_mechanism" title="Higgs mechanism">Higgs mechanism</a>, slightly after but independently<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> from the publications of <a href="/wiki/Peter_Higgs" title="Peter Higgs">Peter Higgs</a> and others. The paper was delayed by the Editorial Office of JETP, and was published only in 1966.<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><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> </p> <div class="mw-heading mw-heading2"><h2 id="Honors_and_awards">Honors and awards</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alexander_Markovich_Polyakov&action=edit&section=2" title="Edit section: Honors and awards"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Alexander Polyakov was awarded the <a href="/wiki/Dirac_Medal_(ICTP)" title="Dirac Medal (ICTP)">Dirac Medal of the ICTP</a> and the <a href="/wiki/Dannie_Heineman_Prize_for_Mathematical_Physics" title="Dannie Heineman Prize for Mathematical Physics">Dannie Heineman Prize for Mathematical Physics</a> in 1986, the <a href="/wiki/Lorentz_Medal" title="Lorentz Medal">Lorentz Medal</a> in 1994, the <a href="/wiki/Oskar_Klein_Memorial_Lecture" title="Oskar Klein Memorial Lecture">Oskar Klein Medal</a> in 1996, the <a href="/wiki/Harvey_Prize" title="Harvey Prize">Harvey Prize</a> in 2010, the <a href="/wiki/Lars_Onsager_Prize" title="Lars Onsager Prize">Lars Onsager Prize</a> (together with <a href="/wiki/Alexander_Belavin" title="Alexander Belavin">A. Belavin</a> and <a href="/wiki/Alexander_Zamolodchikov" title="Alexander Zamolodchikov">A. Zamolodchikov</a>) in 2011 and the <a href="/wiki/Breakthrough_Prize_in_Fundamental_Physics" title="Breakthrough Prize in Fundamental Physics">Breakthrough Prize in Fundamental Physics</a> in 2013. On 19 November 2020 the <a href="/wiki/German_Physical_Society" title="German Physical Society">German Physical Society</a> announced it would award Alexander Polyakov the 2021 <a href="/wiki/Max_Planck_Medal" title="Max Planck Medal">Max Planck Medal</a>. </p><p>Polyakov was elected to the <a href="/wiki/Soviet_Academy_of_Sciences" class="mw-redirect" title="Soviet Academy of Sciences">Soviet Academy of Sciences</a> in 1984,<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> to the <a href="/wiki/French_Academy_of_Sciences" title="French Academy of Sciences">French Academy of Sciences</a> in 1998<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> and the U.S. <a href="/wiki/United_States_National_Academy_of_Sciences" class="mw-redirect" title="United States National Academy of Sciences">National Academy of Sciences</a> (NAS) in 2005.<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> <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> </p> <div class="mw-heading mw-heading2"><h2 id="Political_positions">Political positions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alexander_Markovich_Polyakov&action=edit&section=3" title="Edit section: Political positions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In February-March 2022, he signed an open letter by Russian scientists condemning the <a href="/wiki/2022_Russian_invasion_of_Ukraine" class="mw-redirect" title="2022 Russian invasion of Ukraine">2022 Russian invasion of Ukraine</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> and another open letter by Breakthrough Prize laureates with the same message.<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="Famous_quotes">Famous quotes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alexander_Markovich_Polyakov&action=edit&section=4" title="Edit section: Famous quotes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <blockquote> <p>“<i>The garbage of the past often becomes the treasure of the present (and vice versa).</i>”<sup id="cite_ref-GFS_16-0" class="reference"><a href="#cite_note-GFS-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> </blockquote> <blockquote> <p>“<i>There are no tables for path integrals.</i>” (quoted in <sup id="cite_ref-Auerbach_17-0" class="reference"><a href="#cite_note-Auerbach-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup>) </p> </blockquote> <blockquote> <p>“<i>I wanted to learn about elementary particles by studying boiling water.</i>” <sup id="cite_ref-sasha_18-0" class="reference"><a href="#cite_note-sasha-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> (paraphrased in <sup id="cite_ref-slava_19-0" class="reference"><a href="#cite_note-slava-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup>) </p> </blockquote> <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=Alexander_Markovich_Polyakov&action=edit&section=5" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col"> <ul><li><a href="/wiki/Polyakov_action" title="Polyakov action">Polyakov action</a></li> <li><a href="/wiki/%27t_Hooft%E2%80%93Polyakov_monopole" title="'t Hooft–Polyakov monopole">'t Hooft–Polyakov monopole</a></li> <li><a href="/wiki/BPST_instanton" title="BPST instanton">Belavin–Polyakov–Schwarz–Tyupkin instantons</a></li> <li><a href="/wiki/QCD_vacuum" title="QCD vacuum">QCD vacuum</a></li> <li><a href="/wiki/Conformal_bootstrap" title="Conformal bootstrap">Conformal bootstrap</a></li> <li><a href="/wiki/Liouville_field_theory" title="Liouville field theory">Liouville theory</a></li> <li><a href="/wiki/AdS/CFT_correspondence" title="AdS/CFT correspondence">AdS/CFT correspondence</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alexander_Markovich_Polyakov&action=edit&section=6" 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 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.cs1-maint{color:#18911f}}</style><cite class="citation journal cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110709210059/http://cerncourier.com/cws/article/cern/29554/2">"Princeton celebrates Polyakov's 60th"</a>. <i>CERN Courier</i> (Mar 1): 2. 2006. Archived from <a rel="nofollow" class="external text" href="http://cerncourier.com/cws/article/cern/29554/2">the original</a> on 2011-07-09<span class="reference-accessdate">. Retrieved <span class="nowrap">2007-09-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=CERN+Courier&rft.atitle=Princeton+celebrates+Polyakov%27s+60th&rft.issue=Mar+1&rft.pages=2&rft.date=2006&rft_id=http%3A%2F%2Fcerncourier.com%2Fcws%2Farticle%2Fcern%2F29554%2F2&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlexander+Markovich+Polyakov" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://phy.princeton.edu/people/alexander-polyakov">"Alexander Polyakov | Department of Physics"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Alexander+Polyakov+%26%23124%3B+Department+of+Physics&rft_id=https%3A%2F%2Fphy.princeton.edu%2Fpeople%2Falexander-polyakov&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlexander+Markovich+Polyakov" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBelavin_AAPolyakov_AMSchwartz_ASTyupkin_YS1975" class="citation journal cs1">Belavin AA; Polyakov AM; Schwartz AS; Tyupkin YS (1975). "Pseudoparticle solutions of the Yang-Mills equations". <i>Phys. Lett. B</i>. <b>59</b> (1): 85–7. <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/1975PhLB...59...85B">1975PhLB...59...85B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0370-2693%2875%2990163-X">10.1016/0370-2693(75)90163-X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Lett.+B&rft.atitle=Pseudoparticle+solutions+of+the+Yang-Mills+equations&rft.volume=59&rft.issue=1&rft.pages=85-7&rft.date=1975&rft_id=info%3Adoi%2F10.1016%2F0370-2693%2875%2990163-X&rft_id=info%3Abibcode%2F1975PhLB...59...85B&rft.au=Belavin+AA&rft.au=Polyakov+AM&rft.au=Schwartz+AS&rft.au=Tyupkin+YS&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlexander+Markovich+Polyakov" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPolyakov_AM1977" class="citation journal cs1">Polyakov AM (1977). "Quark confinement and topology of gauge theories". <i>Nucl. Phys. B</i>. <b>120</b> (3): 429–58. <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/1977NuPhB.120..429P">1977NuPhB.120..429P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0550-3213%2877%2990086-4">10.1016/0550-3213(77)90086-4</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nucl.+Phys.+B&rft.atitle=Quark+confinement+and+topology+of+gauge+theories&rft.volume=120&rft.issue=3&rft.pages=429-58&rft.date=1977&rft_id=info%3Adoi%2F10.1016%2F0550-3213%2877%2990086-4&rft_id=info%3Abibcode%2F1977NuPhB.120..429P&rft.au=Polyakov+AM&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlexander+Markovich+Polyakov" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPolyakov_AM1981" class="citation journal cs1">Polyakov AM (1981). "Quantum geometry of bosonic strings". <i>Phys. Lett. B</i>. <b>103</b> (3): 207–10. <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/1981PhLB..103..207P">1981PhLB..103..207P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0370-2693%2881%2990743-7">10.1016/0370-2693(81)90743-7</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Lett.+B&rft.atitle=Quantum+geometry+of+bosonic+strings&rft.volume=103&rft.issue=3&rft.pages=207-10&rft.date=1981&rft_id=info%3Adoi%2F10.1016%2F0370-2693%2881%2990743-7&rft_id=info%3Abibcode%2F1981PhLB..103..207P&rft.au=Polyakov+AM&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlexander+Markovich+Polyakov" class="Z3988"></span></span> </li> <li id="cite_note-a-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-a_6-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBelavin_AAPolyakov_AMZamolodchikov_AB1984" class="citation journal cs1">Belavin AA; Polyakov AM; Zamolodchikov AB (1984). <a rel="nofollow" class="external text" href="https://cds.cern.ch/record/152341">"Infinite conformal symmetry in two-dimensional quantum field theory"</a>. <i>Nucl. Phys. B</i>. <b>241</b> (2): 333–80. <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/1984NuPhB.241..333B">1984NuPhB.241..333B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0550-3213%2884%2990052-X">10.1016/0550-3213(84)90052-X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nucl.+Phys.+B&rft.atitle=Infinite+conformal+symmetry+in+two-dimensional+quantum+field+theory&rft.volume=241&rft.issue=2&rft.pages=333-80&rft.date=1984&rft_id=info%3Adoi%2F10.1016%2F0550-3213%2884%2990052-X&rft_id=info%3Abibcode%2F1984NuPhB.241..333B&rft.au=Belavin+AA&rft.au=Polyakov+AM&rft.au=Zamolodchikov+AB&rft_id=https%3A%2F%2Fcds.cern.ch%2Frecord%2F152341&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlexander+Markovich+Polyakov" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPolyakov1992" class="citation arxiv cs1">Polyakov, A (1992). "A View from the Island". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/hep-th/9211140">hep-th/9211140</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=A+View+from+the+Island&rft.date=1992&rft_id=info%3Aarxiv%2Fhep-th%2F9211140&rft.aulast=Polyakov&rft.aufirst=A&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlexander+Markovich+Polyakov" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">A. A. Migdal and A. M. Polyakov, <a rel="nofollow" class="external text" href="http://www.jetp.ac.ru/cgi-bin/dn/e_024_01_0091.pdf">"Spontaneous Breakdown of Strong Interaction Symmetry and Absence of Massless Particles"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131203014220/http://www.jetp.ac.ru/cgi-bin/dn/e_024_01_0091.pdf">Archived</a> 2013-12-03 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, <i>Soviet Physics JETP</i>, July 1966</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://alexandermigdal.com/paradise-lost/">"Paradise Lost – Alexander A. Migdal"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-11-08</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Paradise+Lost+%E2%80%93+Alexander+A.+Migdal&rft_id=https%3A%2F%2Falexandermigdal.com%2Fparadise-lost%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlexander+Markovich+Polyakov" 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"><a rel="nofollow" class="external text" href="http://www.ras.ru/win/db/show_per.asp?P=.id-617.ln-ru">Alexander M. Polyakov</a>. Site of RAS</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.academie-sciences.fr/fr/Liste-des-membres-de-l-Academie-des-sciences-/-P/alexander-polyakov.html">Alexander Polyakov</a>. Académie des sciences</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"><a rel="nofollow" class="external text" href="http://www.nasonline.org/site/Dir/1028252604?pg=vprof&mbr=1006687&returl=http%3A%2F%2Fwww.nasonline.org%2Fsite%2FDir%2F1028252604">Polyakov, Alexandre</a>. NAS Section: Physics</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 rel="nofollow" class="external text" href="http://news.ictp.it/index.php?p=76">Dirac Medalist Elected to NAS</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070816024552/http://news.ictp.it/index.php?p=76">Archived</a> 2007-08-16 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. ICTP News. 9/5/2005</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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://t-invariant.org/2022/02/we-are-against-war/">"Открытое письмо российских учёных и научных журналистов против войны с Украиной"</a> [An open letter from Russian scientists and scientific journalist against the war in Ukraine] (in Russian). 24 February 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">2 April</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=%D0%9E%D1%82%D0%BA%D1%80%D1%8B%D1%82%D0%BE%D0%B5+%D0%BF%D0%B8%D1%81%D1%8C%D0%BC%D0%BE+%D1%80%D0%BE%D1%81%D1%81%D0%B8%D0%B9%D1%81%D0%BA%D0%B8%D1%85+%D1%83%D1%87%D1%91%D0%BD%D1%8B%D1%85+%D0%B8+%D0%BD%D0%B0%D1%83%D1%87%D0%BD%D1%8B%D1%85+%D0%B6%D1%83%D1%80%D0%BD%D0%B0%D0%BB%D0%B8%D1%81%D1%82%D0%BE%D0%B2+%D0%BF%D1%80%D0%BE%D1%82%D0%B8%D0%B2+%D0%B2%D0%BE%D0%B9%D0%BD%D1%8B+%D1%81+%D0%A3%D0%BA%D1%80%D0%B0%D0%B8%D0%BD%D0%BE%D0%B9&rft.date=2022-02-24&rft_id=https%3A%2F%2Ft-invariant.org%2F2022%2F02%2Fwe-are-against-war%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlexander+Markovich+Polyakov" class="Z3988"></span></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"><a rel="nofollow" class="external text" href="https://breakthroughprize.org/News/69">An open letter from Breakthrough Prize laureates</a></span> </li> <li id="cite_note-GFS-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-GFS_16-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPolyakov1987" class="citation book cs1">Polyakov, Alexander (1987). <i>Gauge Fields and Strings</i>. London, UK: Harwood Academic Publishers. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-7186-0393-0" title="Special:BookSources/978-3-7186-0393-0"><bdi>978-3-7186-0393-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gauge+Fields+and+Strings&rft.place=London%2C+UK&rft.pub=Harwood+Academic+Publishers&rft.date=1987&rft.isbn=978-3-7186-0393-0&rft.aulast=Polyakov&rft.aufirst=Alexander&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlexander+Markovich+Polyakov" class="Z3988"></span></span> </li> <li id="cite_note-Auerbach-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-Auerbach_17-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAuerbach1994" class="citation book cs1">Auerbach, Assa (1994). <i>Interacting Electrons and Quantum Magnetism</i>. New York: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-94286-5" title="Special:BookSources/978-0-387-94286-5"><bdi>978-0-387-94286-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Interacting+Electrons+and+Quantum+Magnetism&rft.place=New+York&rft.pub=Springer&rft.date=1994&rft.isbn=978-0-387-94286-5&rft.aulast=Auerbach&rft.aufirst=Assa&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlexander+Markovich+Polyakov" class="Z3988"></span></span> </li> <li id="cite_note-sasha-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-sasha_18-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPolyakov2003" class="citation web cs1">Polyakov, Alexander (2003). <a rel="nofollow" class="external text" href="https://authors.library.caltech.edu/5456/1/hrst.mit.edu/hrs/renormalization/Polyakov/index.html">"Interview with Alexander Polyakov"</a>. <i>Dibner Institute for the history of science and technology</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2019-10-16</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Dibner+Institute+for+the+history+of+science+and+technology&rft.atitle=Interview+with+Alexander+Polyakov&rft.date=2003&rft.aulast=Polyakov&rft.aufirst=Alexander&rft_id=https%3A%2F%2Fauthors.library.caltech.edu%2F5456%2F1%2Fhrst.mit.edu%2Fhrs%2Frenormalization%2FPolyakov%2Findex.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlexander+Markovich+Polyakov" class="Z3988"></span></span> </li> <li id="cite_note-slava-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-slava_19-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRychkov2019" class="citation web cs1">Rychkov, Slava (2019). <a rel="nofollow" class="external text" href="https://courses.ipht.cnrs.fr/?q=fr/node/226">"IPhT's theoretical physics courses: lorentzian methods in conformal field theory"</a>. <i><a href="/wiki/Institut_de_physique_th%C3%A9orique_-_IPhT_Saclay" class="mw-redirect" title="Institut de physique théorique - IPhT Saclay">Institut de physique théorique - IPhT Saclay</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">2019-10-16</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Institut+de+physique+th%C3%A9orique+-+IPhT+Saclay&rft.atitle=IPhT%27s+theoretical+physics+courses%3A+lorentzian+methods+in+conformal+field+theory&rft.date=2019&rft.aulast=Rychkov&rft.aufirst=Slava&rft_id=https%3A%2F%2Fcourses.ipht.cnrs.fr%2F%3Fq%3Dfr%2Fnode%2F226&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAlexander+Markovich+Polyakov" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alexander_Markovich_Polyakov&action=edit&section=7" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" 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href="/wiki/Richard_Taylor_(mathematician)" title="Richard Taylor (mathematician)">Richard Taylor</a> (2015)</li> <li><a href="/wiki/Ian_Agol" title="Ian Agol">Ian Agol</a> (2016)</li> <li><a href="/wiki/Jean_Bourgain" title="Jean Bourgain">Jean Bourgain</a> (2017)</li> <li><a href="/wiki/Christopher_Hacon" title="Christopher Hacon">Christopher Hacon</a>, <a href="/wiki/James_McKernan" title="James McKernan">James McKernan</a> (2018)</li> <li><a href="/wiki/Vincent_Lafforgue" title="Vincent Lafforgue">Vincent Lafforgue</a> (2019)</li> <li><a href="/wiki/Alex_Eskin" title="Alex Eskin">Alex Eskin</a> (2020)</li> <li><a href="/wiki/Martin_Hairer" title="Martin Hairer">Martin Hairer</a> (2021)</li> <li><a href="/wiki/Takuro_Mochizuki" class="mw-redirect" title="Takuro Mochizuki">Takuro Mochizuki</a> (2022)</li> <li><a href="/wiki/Daniel_A._Spielman" class="mw-redirect" title="Daniel A. Spielman">Daniel A. Spielman</a> (2023)</li> <li><a href="/wiki/Simon_Brendle" title="Simon Brendle">Simon Brendle</a> (2024)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Breakthrough_Prize_in_Fundamental_Physics" title="Breakthrough Prize in Fundamental Physics">Fundamental<br />physics</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/Nima_Arkani-Hamed" title="Nima Arkani-Hamed">Nima Arkani-Hamed</a>, <a href="/wiki/Alan_Guth" title="Alan Guth">Alan Guth</a>, <a href="/wiki/Alexei_Kitaev" title="Alexei Kitaev">Alexei Kitaev</a>, <a href="/wiki/Maxim_Kontsevich" title="Maxim Kontsevich">Maxim Kontsevich</a>, <a href="/wiki/Andrei_Linde" title="Andrei Linde">Andrei Linde</a>, <a href="/wiki/Juan_Mart%C3%ADn_Maldacena" class="mw-redirect" title="Juan Martín Maldacena">Juan Maldacena</a>, <a href="/wiki/Nathan_Seiberg" title="Nathan Seiberg">Nathan Seiberg</a>, <a href="/wiki/Ashoke_Sen" title="Ashoke Sen">Ashoke Sen</a>, <a href="/wiki/Edward_Witten" title="Edward Witten">Edward Witten</a> (2012)</li> <li><i>Special</i>: <a href="/wiki/Stephen_Hawking" title="Stephen Hawking">Stephen Hawking</a>, <a href="/wiki/Peter_Jenni" title="Peter Jenni">Peter Jenni</a>, <a href="/wiki/Fabiola_Gianotti" title="Fabiola Gianotti">Fabiola Gianotti</a> (ATLAS), <a href="/wiki/Michel_Della_Negra" title="Michel Della Negra">Michel Della Negra</a>, <a href="/wiki/Tejinder_Virdee" title="Tejinder Virdee">Tejinder Virdee</a>, <a href="/wiki/Guido_Tonelli" title="Guido Tonelli">Guido Tonelli</a>, <a href="/wiki/Joseph_Incandela" title="Joseph Incandela">Joseph Incandela</a> (CMS) and <a href="/wiki/Lyn_Evans" title="Lyn Evans">Lyn Evans</a> (LHC) (2013)</li> <li><a class="mw-selflink selflink">Alexander Polyakov</a> (2013)</li> <li><a href="/wiki/Michael_Green_(physicist)" title="Michael Green (physicist)">Michael Green</a> and <a href="/wiki/John_Henry_Schwarz" title="John Henry Schwarz">John Henry Schwarz</a> (2014)</li> <li><a href="/wiki/Saul_Perlmutter" title="Saul Perlmutter">Saul Perlmutter</a> and members of the <a href="/wiki/Supernova_Cosmology_Project" title="Supernova Cosmology Project">Supernova Cosmology Project</a>; <a href="/wiki/Brian_Schmidt" title="Brian Schmidt">Brian Schmidt</a>, <a href="/wiki/Adam_Riess" title="Adam Riess">Adam Riess</a> and members of the <a href="/wiki/High-Z_Supernova_Search_Team" title="High-Z Supernova Search Team">High-Z Supernova Team</a> (2015)</li> <li><i>Special</i>: <a href="/wiki/Ronald_Drever" title="Ronald Drever">Ronald Drever</a>, <a href="/wiki/Kip_Thorne" title="Kip Thorne">Kip Thorne</a>, <a href="/wiki/Rainer_Weiss" title="Rainer Weiss">Rainer Weiss</a> and contributors to <a href="/wiki/LIGO" title="LIGO">LIGO</a> project (2016)</li> <li><a href="/wiki/Wang_Yifang" title="Wang Yifang">Yifang Wang</a>, <a href="/wiki/Kam-Biu_Luk" title="Kam-Biu Luk">Kam-Biu Luk</a> and the <a href="/wiki/Daya_Bay_Reactor_Neutrino_Experiment" title="Daya Bay Reactor Neutrino Experiment">Daya Bay team</a>, <a href="/wiki/Atsuto_Suzuki" title="Atsuto Suzuki">Atsuto Suzuki</a> and the <a href="/wiki/Kamioka_Liquid_Scintillator_Antineutrino_Detector" title="Kamioka Liquid Scintillator Antineutrino Detector">KamLAND</a> team, <a href="/wiki/K%C5%8Dichir%C5%8D_Nishikawa" title="Kōichirō Nishikawa">Kōichirō Nishikawa</a> and the <a href="/wiki/K2K_experiment" title="K2K experiment">K2K</a> / <a href="/wiki/T2K_experiment" title="T2K experiment">T2K</a> team, <a href="/wiki/Arthur_B._McDonald" title="Arthur B. McDonald">Arthur B. McDonald</a> and the <a href="/wiki/Sudbury_Neutrino_Observatory" title="Sudbury Neutrino Observatory">Sudbury Neutrino Observatory</a> team, <a href="/wiki/Takaaki_Kajita" title="Takaaki Kajita">Takaaki Kajita</a> and <a href="/wiki/Y%C5%8Dichir%C5%8D_Suzuki" title="Yōichirō Suzuki">Yōichirō Suzuki</a> and the <a href="/wiki/Super-Kamiokande" title="Super-Kamiokande">Super-Kamiokande</a> team (2016)</li> <li><a href="/wiki/Joseph_Polchinski" title="Joseph Polchinski">Joseph Polchinski</a>, <a href="/wiki/Andrew_Strominger" title="Andrew Strominger">Andrew Strominger</a>, <a href="/wiki/Cumrun_Vafa" title="Cumrun Vafa">Cumrun Vafa</a> (2017)</li> <li><a href="/wiki/Charles_L._Bennett" title="Charles L. Bennett">Charles L. Bennett</a>, <a href="/wiki/Gary_Hinshaw" title="Gary Hinshaw">Gary Hinshaw</a>, <a href="/wiki/Norman_Jarosik" title="Norman Jarosik">Norman Jarosik</a>, <a href="/wiki/Lyman_Page" title="Lyman Page">Lyman Page Jr.</a>, <a href="/wiki/David_Spergel" title="David Spergel">David Spergel</a> (2018)</li> <li><i>Special</i>: <a href="/wiki/Jocelyn_Bell_Burnell" title="Jocelyn Bell Burnell">Jocelyn Bell Burnell</a> (2018)</li> <li><a href="/wiki/Charles_L._Kane" title="Charles L. Kane">Charles Kane</a> and <a href="/wiki/Eugene_J._Mele" title="Eugene J. Mele">Eugene Mele</a> (2019)</li> <li><i>Special</i>: <a href="/wiki/Sergio_Ferrara" title="Sergio Ferrara">Sergio Ferrara</a>, <a href="/wiki/Daniel_Z._Freedman" title="Daniel Z. Freedman">Daniel Z. Freedman</a>, <a href="/wiki/Peter_van_Nieuwenhuizen" title="Peter van Nieuwenhuizen">Peter van Nieuwenhuizen</a> (2019)</li> <li><a href="/wiki/The_Event_Horizon_Telescope_Collaboration" class="mw-redirect" title="The Event Horizon Telescope Collaboration">The Event Horizon Telescope Collaboration</a> (2020)</li> <li><a href="/wiki/Eric_Adelberger" class="mw-redirect" title="Eric Adelberger">Eric Adelberger</a>, <a href="/wiki/Jens_H._Gundlach" title="Jens H. Gundlach">Jens H. Gundlach</a> and <a href="/wiki/Blayne_Heckel" title="Blayne Heckel">Blayne Heckel</a> (2021)</li> <li><i>Special</i>: <a href="/wiki/Steven_Weinberg" title="Steven Weinberg">Steven Weinberg</a> (2021)</li> <li><a href="/wiki/Hidetoshi_Katori" title="Hidetoshi Katori">Hidetoshi Katori</a> and <a href="/wiki/Jun_Ye" title="Jun Ye">Jun Ye</a> (2022)</li> <li><a href="/wiki/Charles_H._Bennett_(physicist)" title="Charles H. Bennett (physicist)">Charles H. Bennett</a>, <a href="/wiki/Gilles_Brassard" title="Gilles Brassard">Gilles Brassard</a>, <a href="/wiki/David_Deutsch" title="David Deutsch">David Deutsch</a>, <a href="/wiki/Peter_W._Shor" class="mw-redirect" title="Peter W. Shor">Peter W. Shor</a> (2023)</li> <li><a href="/wiki/John_Cardy" title="John Cardy">John Cardy</a> and <a href="/wiki/Alexander_Zamolodchikov" title="Alexander Zamolodchikov">Alexander Zamolodchikov</a> (2024)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Breakthrough_Prize_in_Life_Sciences" title="Breakthrough Prize in Life Sciences">Life sciences</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/Cornelia_Bargmann" title="Cornelia Bargmann">Cornelia Bargmann</a>, <a href="/wiki/David_Botstein" title="David Botstein">David Botstein</a>, <a href="/wiki/Lewis_C._Cantley" title="Lewis C. Cantley">Lewis C. Cantley</a>, <a href="/wiki/Hans_Clevers" title="Hans Clevers">Hans Clevers</a>, <a href="/wiki/Titia_de_Lange" title="Titia de Lange">Titia de Lange</a>, <a href="/wiki/Napoleone_Ferrara" title="Napoleone Ferrara">Napoleone Ferrara</a>, <a href="/wiki/Eric_Lander" title="Eric Lander">Eric Lander</a>, <a href="/wiki/Charles_Sawyers" title="Charles Sawyers">Charles Sawyers</a>, <a href="/wiki/Robert_Weinberg_(biologist)" title="Robert Weinberg (biologist)">Robert Weinberg</a>, <a href="/wiki/Shinya_Yamanaka" title="Shinya Yamanaka">Shinya Yamanaka</a> and <a href="/wiki/Bert_Vogelstein" title="Bert Vogelstein">Bert Vogelstein</a> (2013)</li> <li><a href="/wiki/James_P._Allison" title="James P. Allison">James P. Allison</a>, <a href="/wiki/Mahlon_DeLong" title="Mahlon DeLong">Mahlon DeLong</a>, <a href="/wiki/Michael_N._Hall" title="Michael N. Hall">Michael N. Hall</a>, <a href="/wiki/Robert_S._Langer" title="Robert S. Langer">Robert S. Langer</a>, <a href="/wiki/Richard_P._Lifton" title="Richard P. Lifton">Richard P. Lifton</a> and <a href="/wiki/Alexander_Varshavsky" title="Alexander Varshavsky">Alexander Varshavsky</a> (2014)</li> <li><a href="/wiki/Alim_Louis_Benabid" title="Alim Louis Benabid">Alim Louis Benabid</a>, <a href="/wiki/Charles_David_Allis" title="Charles David Allis">Charles David Allis</a>, <a href="/wiki/Victor_Ambros" title="Victor Ambros">Victor Ambros</a>, <a href="/wiki/Gary_Ruvkun" title="Gary Ruvkun">Gary Ruvkun</a>, <a href="/wiki/Jennifer_Doudna" title="Jennifer Doudna">Jennifer Doudna</a> and <a href="/wiki/Emmanuelle_Charpentier" title="Emmanuelle Charpentier">Emmanuelle Charpentier</a> (2015)</li> <li><a href="/wiki/Edward_Boyden" title="Edward Boyden">Edward Boyden</a>, <a href="/wiki/Karl_Deisseroth" title="Karl Deisseroth">Karl Deisseroth</a>, <a href="/wiki/John_Hardy_(geneticist)" title="John Hardy (geneticist)">John Hardy</a>, <a href="/wiki/Helen_Hobbs" title="Helen Hobbs">Helen Hobbs</a> and <a href="/wiki/Svante_P%C3%A4%C3%A4bo" title="Svante Pääbo">Svante Pääbo</a> (2016)</li> <li><a href="/wiki/Stephen_Elledge" title="Stephen Elledge">Stephen J. Elledge</a>, <a href="/wiki/Harry_F._Noller" title="Harry F. Noller">Harry F. Noller</a>, <a href="/wiki/Roel_Nusse" title="Roel Nusse">Roeland Nusse</a>, <a href="/wiki/Yoshinori_Ohsumi" title="Yoshinori Ohsumi">Yoshinori Ohsumi</a>, <a href="/wiki/Huda_Zoghbi" title="Huda Zoghbi">Huda Zoghbi</a> (2017)</li> <li><a href="/wiki/Joanne_Chory" title="Joanne Chory">Joanne Chory</a>, <a href="/wiki/Peter_Walter" title="Peter Walter">Peter Walter</a>, <a href="/wiki/Kazutoshi_Mori" title="Kazutoshi Mori">Kazutoshi Mori</a>, <a href="/wiki/Kim_Nasmyth" title="Kim Nasmyth">Kim Nasmyth</a>, <a href="/wiki/Don_W._Cleveland" title="Don W. Cleveland">Don W. Cleveland</a> (2018)</li> <li><a href="/wiki/C._Frank_Bennett" title="C. Frank Bennett">C. Frank Bennett</a> and <a href="/wiki/Adrian_R._Krainer" class="mw-redirect" title="Adrian R. Krainer">Adrian R. Krainer</a>, <a href="/wiki/Angelika_Amon" title="Angelika Amon">Angelika Amon</a>, <a href="/wiki/Xiaowei_Zhuang" title="Xiaowei Zhuang">Xiaowei Zhuang</a>, <a href="/wiki/Zhijian_Chen" title="Zhijian Chen">Zhijian Chen</a> (2019)</li> <li><a href="/wiki/Jeffrey_M._Friedman" title="Jeffrey M. Friedman">Jeffrey M. Friedman</a>, <a href="/wiki/Franz-Ulrich_Hartl" title="Franz-Ulrich Hartl">Franz-Ulrich Hartl</a>, <a href="/wiki/Arthur_L._Horwich" title="Arthur L. Horwich">Arthur L. Horwich</a>, <a href="/wiki/David_Julius" title="David Julius">David Julius</a>, <a href="/wiki/Virginia_Man-Yee_Lee" title="Virginia Man-Yee Lee">Virginia Man-Yee Lee</a> (2020)</li> <li><a href="/wiki/David_Baker_(biochemist)" title="David Baker (biochemist)">David Baker</a>, <a href="/wiki/Catherine_Dulac" title="Catherine Dulac">Catherine Dulac</a>, <a href="/wiki/Dennis_Lo" title="Dennis Lo">Dennis Lo</a>, <a href="/w/index.php?title=Richard_J._Youle&action=edit&redlink=1" class="new" title="Richard J. 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</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 authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q277221#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" 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="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q277221#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="font-size:114%;margin:0 4em"><a 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