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<title>String (physics)</title>

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</style><div role="note" class="hatnote navigation-not-searchable">This article is about quantum strings, the fundamental degrees of freedom in <a href="String_theory" title="String theory">string theory</a>. For an instrumental string, such as a guitar string, see <a href="String_(music)" title="String (music)">String (music)</a>. For other uses, see <a href="String_(disambiguation)" class="mw-redirect mw-disambig" title="String (disambiguation)">String (disambiguation)</a>.</div>

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</style><table class="sidebar sidebar-collapse nomobile nowraplinks hlist"><tbody><tr><th class="sidebar-title"><a href="String_theory" title="String theory">String theory</a></th></tr><tr><td class="sidebar-image"></td></tr><tr><th class="sidebar-heading" style="background: #ddf">

Fundamental objects</th></tr><tr><td class="sidebar-content">

<ul>

<li><a href="Cosmic_string" title="Cosmic string">Cosmic string</a></li>

<li><a href="Brane" title="Brane">Brane</a></li>

<li><a href="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="Bosonic_string_theory" title="Bosonic string theory">Bosonic</a></li>

<li><a href="Superstring_theory" title="Superstring theory">Superstring</a> (<a href="Type_I_string_theory" title="Type I string theory">Type I</a>, <a href="Type_II_string_theory" title="Type II string theory">Type II</a>, <a href="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="S-duality" title="S-duality">S-duality</a></li>

<li><a href="T-duality" title="T-duality">T-duality</a></li>

<li><a href="U-duality" title="U-duality">U-duality</a></li>

<li><a href="M-theory" title="M-theory">M-theory</a></li>

<li><a href="F-theory" title="F-theory">F-theory</a></li>

<li><a href="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="String_phenomenology" title="String phenomenology">Phenomenology</a></li>

<li><a href="String_cosmology" title="String cosmology">Cosmology</a></li>

<li><a href="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="Geometric_Langlands_correspondence" title="Geometric Langlands correspondence">Geometric Langlands correspondence</a></li>

<li><a href="Mirror_symmetry_(string_theory)" title="Mirror symmetry (string theory)">Mirror symmetry</a></li>

<li><a href="Monstrous_moonshine" title="Monstrous moonshine">Monstrous moonshine</a></li>

<li><a href="Vertex_algebra" class="mw-redirect" title="Vertex algebra">Vertex algebra</a></li>

<li><a href="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)"><div class="sidebar-list-title-c">Related concepts</div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;">

<ul><li><a href="Theory_of_everything" title="Theory of everything">Theory of everything</a></li>

<li><a href="Conformal_field_theory" title="Conformal field theory">Conformal field theory</a></li>

<li><a href="Quantum_gravity" title="Quantum gravity">Quantum gravity</a></li>

<li><a href="Supersymmetry" title="Supersymmetry">Supersymmetry</a></li>

<li><a href="Supergravity" title="Supergravity">Supergravity</a></li>

<li><a href="Twistor_string_theory" title="Twistor string theory">Twistor string theory</a></li>

<li><a href="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="Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein theory</a></li>

<li><a href="Multiverse" title="Multiverse">Multiverse</a></li>

<li><a href="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)"><div class="sidebar-list-title-c">Theorists</div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;">

<ul><li><a href="Mina_Aganagi%C4%87" title="Mina Aganagić">Aganagić</a></li>

<li><a href="Nima_Arkani-Hamed" title="Nima Arkani-Hamed">Arkani-Hamed</a></li>

<li><a href="Michael_Atiyah" title="Michael Atiyah">Atiyah</a></li>

<li><a href="Tom_Banks_(physicist)" title="Tom Banks (physicist)">Banks</a></li>

<li><a href="David_Berenstein" title="David Berenstein">Berenstein</a></li>

<li><a href="Raphael_Bousso" title="Raphael Bousso">Bousso</a></li>

<li><a href="Kevin_Costello" title="Kevin Costello">Costello</a></li>

<li><a href="Thomas_Curtright" title="Thomas Curtright">Curtright</a></li>

<li><a href="Robbert_Dijkgraaf" title="Robbert Dijkgraaf">Dijkgraaf</a></li>

<li><a href="Jacques_Distler" title="Jacques Distler">Distler</a></li>

<li><a href="Michael_R._Douglas" title="Michael R. Douglas">Douglas</a></li>

<li><a href="Gia_Dvali" class="mw-redirect" title="Gia Dvali">Dvali</a></li>

<li><a href="Sergio_Ferrara" title="Sergio Ferrara">Ferrara</a></li>

<li><a href="Willy_Fischler" title="Willy Fischler">Fischler</a></li>

<li><a href="Daniel_Friedan" title="Daniel Friedan">Friedan</a></li>

<li><a href="Sylvester_James_Gates" title="Sylvester James Gates">Gates</a></li>

<li><a href="Ferdinando_Gliozzi" title="Ferdinando Gliozzi">Gliozzi</a></li>

<li><a href="Rajesh_Gopakumar" title="Rajesh Gopakumar">Gopakumar</a></li>

<li><a href="Michael_Green_(physicist)" title="Michael Green (physicist)">Green</a></li>

<li><a href="Brian_Greene" title="Brian Greene">Greene</a></li>

<li><a href="David_Gross" title="David Gross">Gross</a></li>

<li><a href="Steven_Gubser" title="Steven Gubser">Gubser</a></li>

<li><a href="Sergei_Gukov" title="Sergei Gukov">Gukov</a></li>

<li><a href="Andrew_J._Hanson" title="Andrew J. Hanson">Hanson</a></li>

<li><a href="Jeffrey_A._Harvey" title="Jeffrey A. Harvey">Harvey</a></li>

<li><a href="Petr_Ho%C5%99ava_(theorist)" class="mw-redirect" title="Petr Hořava (theorist)">Hořava</a></li>

<li><a href="Gary_Horowitz" title="Gary Horowitz">Horowitz</a></li>

<li><a href="Gary_Gibbons" title="Gary Gibbons">Gibbons</a></li>

<li><a href="Shamit_Kachru" title="Shamit Kachru">Kachru</a></li>

<li><a href="Renata_Kallosh" title="Renata Kallosh">Kallosh</a></li>

<li><a href="Theodor_Kaluza" title="Theodor Kaluza">Kaluza</a></li>

<li><a href="Anton_Kapustin" title="Anton Kapustin">Kapustin</a></li>

<li><a href="Igor_Klebanov" title="Igor Klebanov">Klebanov</a></li>

<li><a href="Vadim_Knizhnik" title="Vadim Knizhnik">Knizhnik</a></li>

<li><a href="Maxim_Kontsevich" title="Maxim Kontsevich">Kontsevich</a></li>

<li><a href="Oskar_Klein" title="Oskar Klein">Klein</a></li>

<li><a href="Andrei_Linde" title="Andrei Linde">Linde</a></li>

<li><a href="Juan_Mart%C3%ADn_Maldacena" class="mw-redirect" title="Juan Martín Maldacena">Maldacena</a></li>

<li><a href="Stanley_Mandelstam" title="Stanley Mandelstam">Mandelstam</a></li>

<li><a href="Donald_Marolf" title="Donald Marolf">Marolf</a></li>

<li><a href="Emil_Martinec" title="Emil Martinec">Martinec</a></li>

<li><a href="Shiraz_Minwalla" title="Shiraz Minwalla">Minwalla</a></li>

<li><a href="Greg_Moore_(physicist)" title="Greg Moore (physicist)">Moore</a></li>

<li><a href="Sunil_Mukhi" title="Sunil Mukhi">Mukhi</a></li>

<li><a href="Robert_Myers_(physicist)" title="Robert Myers (physicist)">Myers</a></li>

<li><a href="Dimitri_Nanopoulos" title="Dimitri Nanopoulos">Nanopoulos</a></li>

<li><a href="Hora%C8%9Biu_N%C4%83stase" title="Horațiu Năstase">Năstase</a></li>

<li><a href="Nikita_Nekrasov" title="Nikita Nekrasov">Nekrasov</a></li>

<li><a href="Andr%C3%A9_Neveu" title="André Neveu">Neveu</a></li>

<li><a href="Holger_Bech_Nielsen" title="Holger Bech Nielsen">Nielsen</a></li>

<li><a href="Peter_van_Nieuwenhuizen" title="Peter van Nieuwenhuizen">van Nieuwenhuizen</a></li>

<li><a href="Sergei_Novikov_(mathematician)" title="Sergei Novikov (mathematician)">Novikov</a></li>

<li><a href="David_Olive" title="David Olive">Olive</a></li>

<li><a href="Hirosi_Ooguri" title="Hirosi Ooguri">Ooguri</a></li>

<li><a href="Burt_Ovrut" title="Burt Ovrut">Ovrut</a></li>

<li><a href="Joseph_Polchinski" title="Joseph Polchinski">Polchinski</a></li>

<li><a href="Alexander_Markovich_Polyakov" title="Alexander Markovich Polyakov">Polyakov</a></li>

<li><a href="Arvind_Rajaraman" title="Arvind Rajaraman">Rajaraman</a></li>

<li><a href="Pierre_Ramond" title="Pierre Ramond">Ramond</a></li>

<li><a href="Lisa_Randall" title="Lisa Randall">Randall</a></li>

<li><a href="Seifallah_Randjbar-Daemi" title="Seifallah Randjbar-Daemi">Randjbar-Daemi</a></li>

<li><a href="Martin_Ro%C4%8Dek" title="Martin Roček">Roček</a></li>

<li><a href="Augusto_Sagnotti" title="Augusto Sagnotti">Sagnotti</a></li>

<li><a href="Jo%C3%ABl_Scherk" title="Joël Scherk">Scherk</a></li>

<li><a href="John_Henry_Schwarz" title="John Henry Schwarz">Schwarz</a></li>

<li><a href="Nathan_Seiberg" title="Nathan Seiberg">Seiberg</a></li>

<li><a href="Stephen_Shenker" title="Stephen Shenker">Shenker</a></li>

<li><a href="Warren_Siegel" title="Warren Siegel">Siegel</a></li>

<li><a href="Eva_Silverstein" title="Eva Silverstein">Silverstein</a></li>

<li><a href="Matthias_Staudacher" title="Matthias Staudacher">Staudacher</a></li>

<li><a href="Paul_Steinhardt" title="Paul Steinhardt">Steinhardt</a></li>

<li><a href="Andrew_Strominger" title="Andrew Strominger">Strominger</a></li>

<li><a href="Raman_Sundrum" title="Raman Sundrum">Sundrum</a></li>

<li><a href="Leonard_Susskind" title="Leonard Susskind">Susskind</a></li>

<li><a href="Gerard_'t_Hooft" title="Gerard 't Hooft">'t Hooft</a></li>

<li><a href="Paul_Townsend" title="Paul Townsend">Townsend</a></li>

<li><a href="Sandip_Trivedi" title="Sandip Trivedi">Trivedi</a></li>

<li><a href="Neil_Turok" title="Neil Turok">Turok</a></li>

<li><a href="Gabriele_Veneziano" title="Gabriele Veneziano">Veneziano</a></li>

<li><a href="Erik_Verlinde" title="Erik Verlinde">Verlinde</a></li>

<li><a href="Herman_Verlinde" title="Herman Verlinde">Verlinde</a></li>

<li><a href="Edward_Witten" title="Edward Witten">Witten</a></li>

<li><a href="Tamiaki_Yoneya" title="Tamiaki Yoneya">Yoneya</a></li>

<li><a href="Alexander_Zamolodchikov" title="Alexander Zamolodchikov">Zamolodchikov</a></li>

<li><a href="Alexei_Zamolodchikov" title="Alexei Zamolodchikov">Zamolodchikov</a></li>

<li><a href="Eric_Zaslow" title="Eric Zaslow">Zaslow</a></li>

<li><a href="Bruno_Zumino" title="Bruno Zumino">Zumino</a></li>

<li><a href="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="History_of_string_theory" title="History of string theory">History</a></li>

<li><a href="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;"><style data-mw-deduplicate="TemplateStyles:r1239400231">

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<p>In <a href="Physics" title="Physics">physics</a>, a <b>string</b> is a physical entity postulated in <a href="String_theory" title="String theory">string theory</a> and related subjects. Unlike <a href="Elementary_particle" title="Elementary particle">elementary particles</a>, which are <a href="Zero-dimensional_space" title="Zero-dimensional space">zero-dimensional</a> or point-like by definition, strings are one-dimensional extended entities.<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> Researchers often have an interest in string theories because theories in which the fundamental entities are strings rather than point particles automatically have many properties that some physicists expect to hold in a fundamental theory of physics. Most notably, a theory of strings that evolve and interact according to the rules of <a href="Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> will automatically describe <a href="Quantum_gravity" title="Quantum gravity">quantum gravity</a>.

</p>

<div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2></div>

<p>In string theory, the strings may be open (forming a segment with two endpoints) or closed (forming a loop like a circle) and may have other special properties.<sup id="cite_ref-polchinski1_2-0" class="reference"><a href="#cite_note-polchinski1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Prior to 1995, there were five known versions of string theory incorporating the idea of <a href="Supersymmetry" title="Supersymmetry">supersymmetry</a> (these five are known as <a href="Superstring_theory" title="Superstring theory">superstring theories</a>) and two versions without supersymmetry known as <a href="Bosonic_string_theory" title="Bosonic string theory">bosonic string theories</a>, which differed in the type of strings and in other aspects. Today, these different superstring theories are thought to arise as different limiting cases of a single theory called <a href="M-theory" title="M-theory">M-theory</a>.

</p><p>In string theories of particle physics, the strings are very tiny; much smaller than can be observed in today's particle accelerators. The characteristic length scale of strings is typically on the order of the <a href="Planck_length" class="mw-redirect" title="Planck length">Planck length</a>, about 10<sup>−35</sup> meter, the scale at which the effects of <a href="Quantum_gravity" title="Quantum gravity">quantum gravity</a> are believed to become significant. Therefore on much larger length scales, such as the scales visible in physics laboratories, such entities would appear to be zero-dimensional point particles. Strings are able to vibrate as <a href="Harmonic_oscillator" title="Harmonic oscillator">harmonic oscillators</a>, and different vibrational states of the same string are interpreted as different types of particles. In string theories, strings vibrating at different frequencies constitute the multiple fundamental particles found in the current <a href="Standard_Model" title="Standard Model">Standard Model</a> of particle physics. Strings are also sometimes studied in <a href="Nuclear_physics" title="Nuclear physics">nuclear physics</a> where they are used to model <a href="Flux_tube" title="Flux tube">flux tubes</a>.

</p><p>As the string propagates through <a href="Spacetime" title="Spacetime">spacetime</a>, a string sweeps out a two-dimensional <a href="Surface_(topology)" title="Surface (topology)">surface</a> called its <a href="Worldsheet" title="Worldsheet">worldsheet</a>. This is analogous to the one-dimensional worldline traced out by a point particle. The physics of a string is described by means of a <a href="Two-dimensional_conformal_field_theory" title="Two-dimensional conformal field theory">two-dimensional conformal field theory</a> associated with the worldsheet. The formalism of two-dimensional conformal field theory also has many applications outside of string theory, for example in <a href="Condensed_matter_physics" title="Condensed matter physics">condensed matter physics</a> and parts of <a href="Pure_mathematics" title="Pure mathematics">pure mathematics</a>.

</p>

<div class="mw-heading mw-heading2"><h2 id="Types_of_strings">Types of strings</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Closed_and_open_strings">Closed and open strings</h3></div>

<p>Strings can be either open or closed. A <b>closed string</b> is a string that has no end-points, and therefore is <a href="Topologically_equivalent" class="mw-redirect" title="Topologically equivalent">topologically equivalent</a> to a <a href="Circle" title="Circle">circle</a>. An <b>open string</b>, on the other hand, has two end-points and is topologically equivalent to a line interval. Not all string theories contain open strings, but every theory must contain closed strings, as interactions between open strings can always result in closed strings.

</p><p>The oldest <a href="Superstring_theory" title="Superstring theory">superstring theory</a> containing open strings was <a href="Type_I_string_theory" title="Type I string theory">type I string theory</a>. However, the developments in string theory in the 1990s have shown that the open strings should always be thought of as ending on a new physical degree of freedom called <a href="D-branes" class="mw-redirect" title="D-branes">D-branes</a>, and the spectrum of possibilities for open strings has significantly increased.

</p><p>Open and closed strings are generally associated with characteristic vibrational modes. One of the vibration modes of a closed string can be identified as the <a href="Graviton" title="Graviton">graviton</a>. In certain string theories, the lowest-energy vibration of an open string is a <a href="Tachyon" title="Tachyon">tachyon</a> and can undergo <a href="Tachyon_condensation" title="Tachyon condensation">tachyon condensation</a>. Other vibrational modes of open strings exhibit the properties of <a href="Photon" title="Photon">photons</a> and <a href="Gluon" title="Gluon">gluons</a>.

</p>

<div class="mw-heading mw-heading3"><h3 id="Orientation">Orientation</h3></div>

<p>Strings can also possess an <b>orientation</b>, which can be thought of as an internal "arrow" that distinguishes the string from one with the opposite orientation. By contrast, an <b>unoriented string</b> is one with no such arrow on it.

</p>

<ul><li><a href="Cosmic_string" title="Cosmic string">Cosmic strings</a></li>

<li><a href="Elementary_particle" title="Elementary particle">Elementary particle</a></li>

<li><a href="Brane" title="Brane">Brane</a></li>

<li><a href="D-brane" title="D-brane">D-brane</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFBeckerSchwarzBecker2007" class="citation book cs1">Becker, Katrin; Schwarz, John H.; Becker, Melanie (2007). <i>String theory and M-theory: a modern introduction</i>. Cambridge New York: Cambridge University Press. p. 6. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-511-25653-0</bdi>.</cite></span>

</li>

<li id="cite_note-polchinski1-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-polchinski1_2-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFPolchinski2004" class="citation book cs1">Polchinski, Joseph Gerard (2004). <i>String theory. Vol. 1: An introduction to the bosonic string / Joseph Polchinski</i> (Reprint ed.). Cambridge: Cambridge Univ. Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0521633031</bdi>.</cite></span>

</li>

</ol></div></div>

<ul><li>Schwarz, John (2000). <a rel="nofollow" class="external text" href="http://xxx.uni-augsburg.de/abs/hep-ex/0008017">"Introduction to Superstring Theory"</a>. Retrieved Dec. 12, 2005.</li>

<li><a rel="nofollow" class="external text" href="https://www.pbs.org/wgbh/nova/series/the-elegant-universe/">"NOVA's strings homepage"</a></li></ul>

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</style></div><div role="navigation" class="navbox" aria-labelledby="String_theory190" 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;"><div id="String_theory190" style="font-size:114%;margin:0 4em"><a href="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="Cosmic_string" title="Cosmic string">Cosmic strings</a></li>

<li><a href="History_of_string_theory" title="History of string theory">History of string theory</a>

<ul><li><a href="First_superstring_revolution" class="mw-redirect" title="First superstring revolution">First superstring revolution</a></li>

<li><a href="Second_superstring_revolution" class="mw-redirect" title="Second superstring revolution">Second superstring revolution</a></li></ul></li>

<li><a href="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="Nambu%E2%80%93Goto_action" title="Nambu–Goto action">Nambu–Goto action</a></li>

<li><a href="Polyakov_action" title="Polyakov action">Polyakov action</a></li>

<li><a href="Bosonic_string_theory" title="Bosonic string theory">Bosonic string theory</a></li>

<li><a href="Superstring_theory" title="Superstring theory">Superstring theory</a>

<ul><li><a href="Type_I_string_theory" title="Type I string theory">Type I string</a></li>

<li><a href="Type_II_string_theory" title="Type II string theory">Type II string</a>

<ul><li><a href="Type_II_string_theory" title="Type II string theory">Type IIA string</a></li>

<li><a href="Type_II_string_theory" title="Type II string theory">Type IIB string</a></li></ul></li>

<li><a href="Heterotic_string_theory" title="Heterotic string theory">Heterotic string</a></li></ul></li>

<li><a href="N%3D2_superstring" class="mw-redirect" title="N=2 superstring">N=2 superstring</a></li>

<li><a href="F-theory" title="F-theory">F-theory</a></li>

<li><a href="String_field_theory" title="String field theory">String field theory</a></li>

<li><a href="Matrix_string_theory" title="Matrix string theory">Matrix string theory</a></li>

<li><a href="Non-critical_string_theory" title="Non-critical string theory">Non-critical string theory</a></li>

<li><a href="Non-linear_sigma_model" title="Non-linear sigma model">Non-linear sigma model</a></li>

<li><a href="Tachyon_condensation" title="Tachyon condensation">Tachyon condensation</a></li>

<li><a href="RNS_formalism" title="RNS formalism">RNS formalism</a></li>

<li><a href="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="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="T-duality" title="T-duality">T-duality</a></li>

<li><a href="S-duality" title="S-duality">S-duality</a></li>

<li><a href="U-duality" title="U-duality">U-duality</a></li>

<li><a href="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="Graviton" title="Graviton">Graviton</a></li>

<li><a href="Dilaton" title="Dilaton">Dilaton</a></li>

<li><a href="Tachyon" title="Tachyon">Tachyon</a></li>

<li><a href="Ramond%E2%80%93Ramond_field" title="Ramond–Ramond field">Ramond–Ramond field</a></li>

<li><a href="Kalb%E2%80%93Ramond_field" title="Kalb–Ramond field">Kalb–Ramond field</a></li>

<li><a href="Magnetic_monopole" title="Magnetic monopole">Magnetic monopole</a></li>

<li><a href="Dual_graviton" title="Dual graviton">Dual graviton</a></li>

<li><a href="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="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="D-brane" title="D-brane">D-brane</a></li>

<li><a href="NS5-brane" title="NS5-brane">NS5-brane</a></li>

<li><a href="M2-brane" title="M2-brane">M2-brane</a></li>

<li><a href="M5-brane" title="M5-brane">M5-brane</a></li>

<li><a href="S-brane" title="S-brane">S-brane</a></li>

<li><a href="Black_brane" title="Black brane">Black brane</a></li>

<li><a href="Black_hole" title="Black hole">Black holes</a></li>

<li><a href="Black_string" class="mw-redirect" title="Black string">Black string</a></li>

<li><a href="Brane_cosmology" title="Brane cosmology">Brane cosmology</a></li>

<li><a href="Quiver_diagram" title="Quiver diagram">Quiver diagram</a></li>

<li><a href="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="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="Virasoro_algebra" title="Virasoro algebra">Virasoro algebra</a></li>

<li><a href="Mirror_symmetry_(string_theory)" title="Mirror symmetry (string theory)">Mirror symmetry</a></li>

<li><a href="Conformal_anomaly" title="Conformal anomaly">Conformal anomaly</a></li>

<li><a href="Conformal_symmetry" title="Conformal symmetry">Conformal algebra</a></li>

<li><a href="Superconformal_algebra" title="Superconformal algebra">Superconformal algebra</a></li>

<li><a href="Vertex_operator_algebra" title="Vertex operator algebra">Vertex operator algebra</a></li>

<li><a href="Loop_algebra" title="Loop algebra">Loop algebra</a></li>

<li><a href="Kac%E2%80%93Moody_algebra" title="Kac–Moody algebra">Kac–Moody algebra</a></li>

<li><a href="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="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="Anomaly_(physics)" title="Anomaly (physics)">Anomalies</a></li>

<li><a href="Instanton" title="Instanton">Instantons</a></li>

<li><a href="Chern%E2%80%93Simons_form" title="Chern–Simons form">Chern–Simons form</a></li>

<li><a href="Bogomol'nyi%E2%80%93Prasad%E2%80%93Sommerfield_bound" title="Bogomol'nyi–Prasad–Sommerfield bound">Bogomol'nyi–Prasad–Sommerfield bound</a></li>

<li><a href="Exceptional_Lie_group" class="mw-redirect" title="Exceptional Lie group">Exceptional Lie groups</a> (<a href="G2_(mathematics)" title="G2 (mathematics)">G<sub>2</sub></a>, <a href="F4_(mathematics)" title="F4 (mathematics)">F<sub>4</sub></a>, <a href="E6_(mathematics)" title="E6 (mathematics)">E<sub>6</sub></a>, <a href="E7_(mathematics)" title="E7 (mathematics)">E<sub>7</sub></a>, <a href="E8_(mathematics)" title="E8 (mathematics)">E<sub>8</sub></a>)</li>

<li><a href="ADE_classification" title="ADE classification">ADE classification</a></li>

<li><a href="Dirac_string" title="Dirac string">Dirac string</a></li>

<li><a href="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="Worldsheet" title="Worldsheet">Worldsheet</a></li>

<li><a href="Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein theory</a></li>

<li><a href="Compactification_(physics)" title="Compactification (physics)">Compactification</a></li>

<li><a href="Why_10_dimensions" class="mw-redirect" title="Why 10 dimensions">Why 10 dimensions</a>?</li>

<li><a href="K%C3%A4hler_manifold" title="Kähler manifold">Kähler manifold</a></li>

<li><a href="Ricci-flat_manifold" title="Ricci-flat manifold">Ricci-flat manifold</a>

<ul><li><a href="Calabi%E2%80%93Yau_manifold" title="Calabi–Yau manifold">Calabi–Yau manifold</a></li>

<li><a href="Hyperk%C3%A4hler_manifold" title="Hyperkähler manifold">Hyperkähler manifold</a>

<ul><li><a href="K3_surface" title="K3 surface">K3 surface</a></li></ul></li>

<li><a href="G2_manifold" title="G2 manifold">G<sub>2</sub> manifold</a></li>

<li><a href="Spin(7)-manifold" title="Spin(7)-manifold">Spin(7)-manifold</a></li></ul></li>

<li><a href="Generalized_complex_structure" title="Generalized complex structure">Generalized complex manifold</a></li>

<li><a href="Orbifold" title="Orbifold">Orbifold</a></li>

<li><a href="Conifold" title="Conifold">Conifold</a></li>

<li><a href="Orientifold" title="Orientifold">Orientifold</a></li>

<li><a href="Moduli_space" title="Moduli space">Moduli space</a></li>

<li><a href="Ho%C5%99ava%E2%80%93Witten_theory" title="Hořava–Witten theory">Hořava–Witten theory</a></li>

<li><a href="K-theory_(physics)" title="K-theory (physics)">K-theory (physics)</a></li>

<li><a href="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="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="Supergravity" title="Supergravity">Supergravity</a></li>

<li><a href="Eleven-dimensional_supergravity" title="Eleven-dimensional supergravity">Eleven-dimensional supergravity</a></li>

<li><a href="Type_I_supergravity" title="Type I supergravity">Type I supergravity</a></li>

<li><a href="Type_IIA_supergravity" title="Type IIA supergravity">Type IIA supergravity</a></li>

<li><a href="Type_IIB_supergravity" title="Type IIB supergravity">Type IIB supergravity</a></li>

<li><a href="Superspace" title="Superspace">Superspace</a></li>

<li><a href="Lie_superalgebra" title="Lie superalgebra">Lie superalgebra</a></li>

<li><a href="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="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="Holographic_principle" title="Holographic principle">Holographic principle</a></li>

<li><a href="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="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="Matrix_theory_(physics)" title="Matrix theory (physics)">Matrix theory</a></li>

<li><a href="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">