String theory: Difference between revisions

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{{shortShort description|Theory of subatomic structure}}

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{{seeintroSeeintro|Introduction to M-theory}}

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{{String theory}}

In [[physics]], '''string theory''' is a [[Mathematical theory|theoretical framework]] in which the [[Point particle|point-like particles]] of [[particle physics]] are replaced by [[Dimension (mathematics and physics)|one-dimensional]] objects called [[String (physics)|strings]]. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks justacts like an ordinarya particle, with its [[mass]], [[charge (physics)|charge]], and other properties determined by the [[vibration]]al state of the string. In string theory, one of the many vibrational states of the string corresponds to the [[graviton]], a [[quantum mechanics|quantum mechanical]] particle that carries the [[gravity|gravitational force]]. Thus, string theory is a theory of [[quantum gravity]].

String theory is a broad and varied subject that attempts to address a number of deep questions of [[fundamental physics]]. String theory has contributed a number of advances to [[mathematical physics]], which have been applied to a variety of problems in [[black hole]] physics, early universe [[Physical cosmology|cosmology]], [[nuclear physics]], and [[condensed matter physics]], and it has stimulated a number of major developments in [[pure mathematics]]. Because string theory potentially provides a unified description of gravity and particle physics, it is a candidate for a [[theory of everything]], a self-contained [[mathematical model]] that describes all [[Fundamental interaction|fundamental force]]s and forms of [[matter]]. Despite much work on these problems, it is not known to what extent string theory describes the real world or how much freedom the theory allows in the choice of its details.

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In the 20th century, two theoretical frameworks emerged for formulating the laws of physics. The first is [[Albert Einstein]]'s [[general theory of relativity]], a theory that explains the force of [[gravity]] and the structure of [[spacetime]] at the macro-level. The other is [[quantum mechanics]], a completely different formulation, which uses known [[probability]] principles to describe physical phenomena at the micro-level. By the late 1970s, these two frameworks had proven to be sufficient to explain most of the observed features of the [[universe]], from [[elementary particle]]s to [[atom]]s to the evolution of stars and the universe as a whole.<ref name="Becker, Becker 2007, p. 1">[[#Becker|Becker, Becker and Schwarz]], p. 1</ref>

In spite of these successes, there are still many problems that remain to be solved. One of the deepest problems in modern physics is the problem of [[quantum gravity]].<ref name="Becker, Becker 2007, p. 1"/> The general theory of relativity is formulated within the framework of [[classical physics]], whereas the other [[fundamental interaction|fundamental forces]] are described within the framework of quantum mechanics. A quantum theory of gravity is needed in order to reconcile general relativity with the principles of quantum mechanics, but difficulties arise when one attempts to apply the usual prescriptions of quantum theory to the force of gravity.<ref>[[#Zwiebach|Zwiebach]], p. 6</ref> In addition to the problem of developing a consistent theory of quantum gravity, there are many other fundamental problems in the physics of [[atomic nucleus|atomic nuclei]], [[black hole]]s, and the early universe.{{efn|For example, physicists are still working to understand the phenomenon of [[quark confinement]], the paradoxes of [[black holes]], and the origin of [[dark energy]].}}

String theory is a [[mathematical theory|theoretical framework]] that attempts to address these questions.

String theory is a [[mathematical theory|theoretical framework]] that attempts to address these questions and many others. The starting point for string theory is the idea that the [[point particle|point-like particles]] of [[particle physics]] can also be modeled as one-dimensional objects called [[string (physics)|strings]]. String theory describes how strings propagate through space and interact with each other. In a given version of string theory, there is only one kind of string, which may look like a small loop or segment of ordinary string, and it can [[vibration|vibrate]] in different ways. On distance scales larger than the string scale, a string will look just like an ordinary particle consistent with non-string models of elementary particles, with its [[mass]], [[charge (physics)|charge]], and other properties determined by the vibrational state of the string. String theory's application as a form of quantum gravity proposes a vibrational state responsible for the [[graviton]], a yet unproven quantum particle that is theorized to carry gravitational force.<ref name="Becker, Becker 2007, pp. 2">[[#Becker|Becker, Becker and Schwarz]], pp. 2–3</ref>

String theory is a [[mathematical theory|theoretical framework]] that attempts to address these questions and many others. The starting point for string theory is the idea that the [[point particle|point-like particles]] of [[particle physics]] can also be modeled as one-dimensional objects called [[string (physics)|strings]]. String theory describes how strings propagate through space and interact with each other. In a given version of string theory, there is only one kind of string, which may look like a small loop or segment of ordinary string, and it can [[vibration|vibrate]] in different ways. On distance scales larger than the string scale, a string will look just like an ordinary particle consistent with non-string models of elementary particles, with its [[mass]], [[charge (physics)|charge]], and other properties determined by the vibrational state of the string. String theory's application as a form of quantum gravity proposes a vibrational state responsible for the [[graviton]], a yet unproven quantum particle that is theorized to carry gravitational force.<ref name="Becker, Becker 2007, pp. 2">[[#Becker|Becker, Becker and Schwarz]], pp. 2–3</ref>

One of the main developments of the past several decades in string theory was the discovery of certain 'dualities', mathematical transformations that identify one physical theory with another. Physicists studying string theory have discovered a number of these dualities between different versions of string theory, and this has led to the conjecture that all consistent versions of string theory are subsumed in a single framework known as [[M-theory]].<ref>[[#Becker|Becker, Becker and Schwarz]], pp. 9–12</ref>

One of the main developments of the past several decades in string theory was the discovery of certain 'dualities'—mathematical transformations that identify one physical theory with another. Physicists studying string theory have discovered a number of these dualities between different versions of string theory, and this has led to the conjecture that all consistent versions of string theory are subsumed in a single framework known as [[M-theory]].<ref>[[#Becker|Becker, Becker and Schwarz]], pp. 9–12</ref>

Studies of string theory have also yielded a number of results on the nature of black holes and the gravitational interaction. There are certain paradoxes that arise when one attempts to understand the quantum aspects of black holes, and work on string theory has attempted to clarify these issues. In late 1997 this line of work culminated in the discovery of the [[anti-de Sitter/conformal field theory correspondence]] or (AdS/CFT for short).<ref>[[#Becker|Becker, Becker and Schwarz]], pp. 14–15</ref> This is a theoretical result that relates string theory to other physical theories which are better understood theoretically. The AdS/CFT correspondence has implications for the study of black holes and quantum gravity, and it has been applied to other subjects, including [[nuclear physics|nuclear]]<ref name="Klebanov and Maldacena 2009"/> and [[condensed matter physics]].<ref name="Merali 2011"/><ref name=Sachdev/>

Since string theory incorporates all of the fundamental interactions, including gravity, many physicists hope that it will eventually be developed to the point where it fully describes our universe, making it a [[theory of everything]]. One of the goals of current research in string theory is to find a solution of the theory that reproduces the observed spectrum of elementary particles, with a small [[cosmological constant]], containing [[dark matter]] and a plausible mechanism for [[cosmic inflation]]. While there has been progress toward these goals, it is not known to what extent string theory describes the real world or how much freedom the theory allows in the choice of details.<ref>[[#Becker|Becker, Becker and Schwarz]], pp. 3, 15–16</ref>

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=== Dualities ===

[[File:Dualities in String Theory.svg|right|thumb|alt=A diagram indicating the relationships between M-theory and the five superstring theories.|thumb|upright=2|A diagram of string theory dualities. Blue edges indicate [[S-duality]]. Red edges indicate [[T-duality]].]]

{{main|S-duality|T-duality}}

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In the branch of physics called [[statistical mechanics]], [[entropy]] is a measure of the randomness or disorder of a physical system. This concept was studied in the 1870s by the Austrian physicist [[Ludwig Boltzmann]], who showed that the [[thermodynamics|thermodynamic]] properties of a [[gas]] could be derived from the combined properties of its many constituent [[molecule]]s. Boltzmann argued that by averaging the behaviors of all the different molecules in a gas, one can understand macroscopic properties such as volume, temperature, and pressure. In addition, this perspective led him to give a precise definition of entropy as the [[natural logarithm]] of the number of different states of the molecules (also called ''microstates'') that give rise to the same macroscopic features.<ref>[[#Yau|Yau and Nadis]], pp. 187–188</ref>

In the twentieth century, physicists began to apply the same concepts to black holes. In most systems such as gases, the entropy scales with the volume. In the 1970s, the physicist [[Jacob Bekenstein]] suggested that the entropy of a black hole is instead proportional to the ''surface area'' of its [[event horizon]], the boundary beyond which matter and radiation aremay lost toescape its gravitational attraction.<ref name=Bekenstein/> When combined with ideas of the physicist [[Stephen Hawking]],<ref name=Hawking1975/> Bekenstein's work yielded a precise formula for the entropy of a black hole. The [[Bekenstein–Hawking formula]] expresses the entropy {{math|''S''}} as

: <math>S= \frac{c^3kA}{4\hbar G}</math>

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{{main|AdS/CFT correspondence}}

One approach to formulating string theory and studying its properties is provided by the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. This is a theoretical result whichthat implies that string theory is in some cases equivalent to a quantum field theory. In addition to providing insights into the mathematical structure of string theory, the AdS/CFT correspondence has shed light on many aspects of quantum field theory in regimes where traditional calculational techniques are ineffective.<ref name="Klebanov and Maldacena 2009"/> The AdS/CFT correspondence was first proposed by [[Juan Maldacena]] in late 1997.<ref name=Maldacena1998/> Important aspects of the correspondence were elaborated in articles by [[Steven Gubser]], [[Igor Klebanov]], and [[Alexander Markovich Polyakov]],<ref name=Gubser/> and by Edward Witten.<ref name=Witten1998/> By 2010, Maldacena's article had over 7000 citations, becoming the most highly cited article in the field of [[high energy physics]].{{efn|{{cite web |url=http://www.slac.stanford.edu/spires/topcites/2010/eprints/to_hep-th_annual.shtml |title=Top Cited Articles during 2010 in hep-th |author=<!--Staff writer(s); no by-line.--> |access-date=25 July 2013}}}}

=== Overview of the correspondence ===

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One can imagine a stack of hyperbolic disks where each disk represents the state of the universe at a given time. The resulting geometric object is three-dimensional anti-de Sitter space.<ref name="Maldacena 2005, p. 60"/> It looks like a solid [[cylinder (geometry)|cylinder]] in which any [[cross section (geometry)|cross section]] is a copy of the hyperbolic disk. Time runs along the vertical direction in this picture. The surface of this cylinder plays an important role in the AdS/CFT correspondence. As with the hyperbolic plane, anti-de Sitter space is [[curvature|curved]] in such a way that any point in the interior is actually infinitely far from this boundary surface.<ref name="Maldacena 2005, p. 61"/>

[[File:AdS3.svg|thumb|right|alt=A cylinder formed by stacking copies of the disk illustrated in the previous figure.|thumb|upright=1.6|Three-dimensional [[anti-de Sitter space]] is like a stack of [[Poincaré disk model|hyperbolic disks]], each one representing the state of the universe at a given time. The resulting [[spacetime]] looks like a solid [[cylinder (geometry)|cylinder]].]]

This construction describes a hypothetical universe with only two space dimensions and one time dimension, but it can be generalized to any number of dimensions. Indeed, hyperbolic space can have more than two dimensions and one can "stack up" copies of hyperbolic space to get higher-dimensional models of anti-de Sitter space.<ref name="Maldacena 2005, p. 60"/>

An important feature of anti-de Sitter space is its boundary (which looks like a cylinder in the case of three-dimensional anti-de Sitter space). One property of this boundary is that, within a small region on the surface around any given point, it looks just like [[Minkowski space]], the model of spacetime used in nongravitationalnon-gravitational physics.<ref>[[#Zwiebach|Zwiebach]], p. 552</ref> One can therefore consider an auxiliary theory in which "spacetime" is given by the boundary of anti-de Sitter space. This observation is the starting point for AdS/CFT correspondence, which states that the boundary of anti-de Sitter space can be regarded as the "spacetime" for a quantum field theory. The claim is that this quantum field theory is equivalent to a gravitational theory, such as string theory, in the bulk anti-de Sitter space in the sense that there is a "dictionary" for translating entities and calculations in one theory into their counterparts in the other theory. For example, a single particle in the gravitational theory might correspond to some collection of particles in the boundary theory. In addition, the predictions in the two theories are quantitatively identical so that if two particles have a 40 percent chance of colliding in the gravitational theory, then the corresponding collections in the boundary theory would also have a 40 percent chance of colliding.<ref>[[#Maldacena2005|Maldacena 2005]], pp. 61–62</ref>

=== Applications to quantum gravity ===

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The currently accepted theory describing elementary particles and their interactions is known as the [[standard model of particle physics]]. This theory provides a unified description of three of the fundamental forces of nature: electromagnetism and the strong and weak nuclear forces. Despite its remarkable success in explaining a wide range of physical phenomena, the standard model cannot be a complete description of reality. This is because the standard model fails to incorporate the force of gravity and because of problems such as the [[hierarchy problem]] and the inability to explain the structure of fermion masses or dark matter.

String theory has been used to construct a variety of models of particle physics going beyond the standard model. Typically, such models are based on the idea of compactification. Starting with the ten- or eleven-dimensional spacetime of string or M-theory, physicists postulate a shape for the extra dimensions. By choosing this shape appropriately, they can construct models roughly similar to the standard model of particle physics, together with additional undiscovered particles.<ref name=Candelas1985/> One popular way of deriving realistic physics from string theory is to start with the heterotic theory in ten dimensions and assume that the six extra dimensions of spacetime are shaped like a six-dimensional Calabi–Yau manifold. Such compactifications offer many ways of extracting realistic physics from string theory.<ref>{{cite arXiv|last1=Cvetic|first1=M|authorlink1=Mirjam Cvetič|last2=Halverson|first2=J.|authorlink2=|last3=Shiu|first3=G.|authorlink3=Gary Shiu|last4=Taylor|first4=W.|authorlink4=|date=2022|title=Snowmass White Paper: String Theory and Particle Physics|pages=|class=hep-th|eprint=2204.01742}}</ref> Other similar methods can be used to construct realistic or semi-realistic models of our four-dimensional world based on M-theory.<ref>[[#Yau|Yau and Nadis]], pp. 147–150</ref>

=== Cosmology ===

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In 1992, [[Richard Borcherds]] constructed a bridge between the theory of modular functions and finite groups and, in the process, explained the observations of McKay and Thompson.<ref>[[#Gannon|Gannon]], p. 8</ref><ref name=Borcherds/> Borcherds' work used ideas from string theory in an essential way, extending earlier results of [[Igor Frenkel]], [[James Lepowsky]], and [[Arne Meurman]], who had realized the monster group as the symmetries of a particular{{which|date=February 2016}} version of string theory.<ref name=FLM/> In 1998, Borcherds was awarded the [[Fields medal]] for his work.<ref>[[#Gannon|Gannon]], p. 11</ref>

Since the 1990s, the connection between string theory and moonshine has led to further results in mathematics and physics.<ref name="Klarreich 2015"/> In 2010, physicists [[Tohru Eguchi]], [[Hirosi Ooguri]], and [[Yuji Tachikawa (physicist)|Yuji Tachikawa]] discovered connections between a different sporadic group, the [[Mathieu group M24|Mathieu group {{math|''M''₂₄}}]], and a certain version{{which|date=November 2016}} of string theory.<ref name=EOT/> [[Miranda Cheng]], John Duncan, and [[Jeffrey A. Harvey]] proposed a generalization of this moonshine phenomenon called [[umbral moonshine]],<ref name=CDH/> and their conjecture was proved mathematically by Duncan, Michael Griffin, and [[Ken Ono]].<ref name=DGO/> Witten has also speculated that the version of string theory appearing in monstrous moonshine might be related to a certain simplified model of gravity in three spacetime dimensions.<ref name=Witten2007/>

== History ==

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== Notes ==

{{Notelist}}

{{notelist}}

{{reflist|group=note}}

== References ==

{{reflist|30em|refs=

<ref name="Aspinwall et al. 2009">{{cite book |editor1-first=Paul |editor1-last=Aspinwall |editor2-first=Tom |editor2-last=Bridgeland |editor3-first=Alastair |editor3-last=Craw |editor4-first=Michael |editor4-last=Douglas |editor5-first=Mark |editor5-last=Gross |editor6-first=Anton |editor6-last=Kapustin |editor7-first=Gregory |editor7-last=Moore |editor8-first=Graeme |editor8-last=Segal |editor9-first=Balázs |editor9-last=Szendröi |editor10-first=P.M.H. |editor10-last=Wilson |title=Dirichlet Branes and Mirror Symmetry |year=2009 |publisher=American Mathematical Society | series = [[Clay Mathematics Monographs]] | volume = 4 | isbn=978-0-8218-3848-8|page=13}}</ref>

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<ref name=Nekrasov>{{cite journal |last1=Nekrasov |first1=Nikita |last2=Schwarz |first2=Albert |date=1998 |title=Instantons on noncommutative {{math|'''R'''⁴}} and (2,0) superconformal six dimensional theory |journal=Communications in Mathematical Physics |volume=198 |issue=3 |pages=689–703 |doi=10.1007/s002200050490|bibcode=1998CMaPh.198..689N |arxiv = hep-th/9802068 |s2cid=14125789 }}</ref>

<ref name="Polchinski 2007">{{cite journal |last1=Polchinski |first1=Joseph |title=All Strung Out? |journal=American Scientist |volume=95 |pages=72 |date=2007 |url=http://www.americanscientist.org/bookshelf/pub/all-strung-out |access-date=29 December 2016|doi=10.1511/2007.63.72 |url-access=subscription }}</ref>

<ref name=Randall>{{cite journal |last1=Randall |first1=Lisa |last2=Sundrum |first2=Raman |date=1999 |title=An alternative to compactification |journal=Physical Review Letters |volume=83 |issue=23 |pages=4690–4693 |doi=10.1103/PhysRevLett.83.4690 |arxiv=hep-th/9906064 |bibcode = 1999PhRvL..83.4690R |s2cid=18530420 }}</ref>

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===Bibliography===

{{refbeginRefbegin|30em}}

{{refbegin|30em}}

* {{cite book|ref=Becker |last1=Becker |first1=Katrin |last2=Becker |first2=Melanie |author-link2=Melanie Becker|last3=Schwarz |first3=John |title=String theory and M-theory: A modern introduction |date=2007 |publisher=Cambridge University Press |isbn=978-0-521-86069-7}}

* {{cite journal |ref=Duff1998|last1=Duff |first1=Michael |date=1998 |title=The theory formerly known as strings |journal=Scientific American |volume=278 |issue=2 |pages=64–9 |doi=10.1038/scientificamerican0298-64|bibcode = 1998SciAm.278b..64D }}

* {{cite book |ref=Gannon|last1=Gannon |first1=Terry |title=Moonshine Beyond the Monster: The Bridge Connecting Algebra, Modular Forms, and Physics |date=2023 |publisher=Cambridge University Press|bibcode=2023mbmb.book.....G }}

* {{cite book |ref=Hori|editor1-first=Kentaro |editor1-last=Hori |editor2-first=Sheldon |editor2-last=Katz |editor3-first=Albrecht |editor3-last=Klemm |editor4-first=Rahul |editor4-last=Pandharipande |editor5-first=Richard |editor5-last=Thomas |editor6-first=Cumrun |editor6-last=Vafa |editor7-first=Ravi |editor7-last=Vakil |editor8-first=Eric |editor8-last=Zaslow |title=Mirror Symmetry |year=2003 |series=[[Clay Mathematics Monographs]]|volume=1|publisher=American Mathematical Society |url=http://math.stanford.edu/~vakil/files/mirrorfinal.pdf |isbn=978-0-8218-2955-4 |url-status=dead |archive-url=https://web.archive.org/web/20060919020706/http://math.stanford.edu/~vakil/files/mirrorfinal.pdf |archive-date=2006-09-19 }}

* {{cite journal|ref=Maldacena2005|title=The Illusion of Gravity |last=Maldacena |first=Juan |date=2005 |journal=Scientific American |url=http://www.sns.ias.edu/~malda/sciam-maldacena-3a.pdf |access-date=29 December 2016 |bibcode=2005SciAm.293e..56M |volume=293 |pages=56–63 |doi=10.1038/scientificamerican1105-56 |issue=5 |pmid=16318027 |url-status=dead |archive-url=https://web.archive.org/web/20141101181409/http://www.sns.ias.edu/~malda/sciam-maldacena-3a.pdf |archive-date=November 1, 2014 }}

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* {{Cite book|ref=Yau| first1 = Shing-Tung | last1 = Yau | first2 = Steve | last2 = Nadis | year = 2010 | title = The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions | publisher = Basic Books | isbn = 978-0-465-02023-2 }}

* {{cite book |ref=Zwiebach|last1=Zwiebach |first1=Barton |title=A First Course in String Theory |date=2009 |publisher=Cambridge University Press |isbn=978-0-521-88032-9}}

{{refendRefend}}

== Further reading ==

=== Popular science ===

* {{Cite book| first = Brian | last = Greene | year = 2003 | title = The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory | publisher = W.W. Norton & Company | ___location = New York | isbn = 978-0-393-05858-1 | title-link = The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory }}

* {{Cite book| first = Brian | last = Greene | year = 2004 | title = The Fabric of the Cosmos: Space, Time, and the Texture of Reality | publisher = Alfred A. Knopf | ___location = New York | isbn = 978-0-375-41288-2 | title-link = The Fabric of the Cosmos: Space, Time, and the Texture of Reality | bibcode = 2004fcst.book.....G }}

* {{cite book | last=Gubser | first=Steven Scott | title=The Little Book of String Theory | publisher=Princeton University Press | publication-place=Princeton, N. J. | date=2010 | isbn=978-0-691-14289-0}}

* {{Cite book| first = Roger | last = Penrose | year = 2005 | title = The Road to Reality: A Complete Guide to the Laws of the Universe | publisher = Knopf | isbn = 978-0-679-45443-4 | title-link = The Road to Reality: A Complete Guide to the Laws of the Universe }}

* {{Cite book| first = Lee | last = Smolin | year = 2006 | title = The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next | publisher = Houghton Mifflin Co. | ___location = New York | isbn = 978-0-618-55105-7 | title-link = The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next }}

* {{Citecite book |first=Peter |last=Woit |year first=2006Peter | title=Not Even Wrong: The Failure of String Theory And the Search for Unity in Physical Law | publisher=New York: Basic Books |___location publication-place=London,New England:York Jonathan| Cape &date=2006-09-04 | isbn=978-0-465-09275-8 <!--| bothoclc=67840232 are| correcturl=https://www.worldcat.org/title/67840232 | access-date=2025->05-31}} - UK edition published by Jonathan Cape, London, 2006

=== Textbooks ===

* {{cite book |last1=Becker |first1=K. |last2=Becker |first2=M. |last3=Schwarz |first3=J. H. |title=String Theory and M-Theory: A Modern Introduction |publisher=Cambridge University Press |date=2006 |isbn=978-0521860697}}

* {{cite book |last1=Blumenhagen |first1=R. |last2=Lüst |first2=D. |last3=Theisen |first3=S. |title=Basic Concepts of String Theory |publisher=Springer |date=2012 |isbn=978-3642294969 }}

* {{cite book |last1=Green |first1=Michael |last2=Schwarz |first2=John |last3=Witten |first3=Edward |title=Superstring theory. Vol.Theory |volume=1: ''Introduction'' |publisher=Cambridge University Press |date=2012 |isbn=978-1107029118 }}

* {{cite book |last1=Green |first1=Michael |last2=Schwarz |first2=John |last3=Witten |first3=Edward |title=Superstring theory. Vol.Theory |volume=2: ''Loop amplitudes, anomalies and phenomenology'' |publisher=Cambridge University Press |date=2012 |isbn=978-1107029132 }}

* {{cite book |last1=Ibáñez |first1=L.E. |last2=Uranga |first2=A.M. |title=String Theory and Particle Physics: An Introduction to String Phenomenology |publisher=Cambridge University Press |date=2012 |isbn=978-0521517522 }}

* {{cite book |last1=Kiritsis |first1=E. |title=String Theory in a Nutshell |publisher=Princeton University Press |date=2019 |isbn=978-0691155791 }}

* {{cite book |last=Ortín |first=T. |title=Gravity and Strings |publisher=Cambridge University Press |date=2015 |isbn=978-0521768139 }}

* {{cite book |last1=Polchinski |first1=Joseph |year=1998 |title=String Theory Vol. |volume=1: ''An Introduction to the Bosonic String'' |publisher=Cambridge University Press |isbn=978-0-521-63303-1}}

* {{cite book |last=Polchinski |first=Joseph |year=1998 |title=String Theory Vol. |volume=2: ''Superstring Theory and Beyond'' |publisher=Cambridge University Press |isbn=978-0-521-63304-8}}

* {{cite book |last1=West|first1=P. |title=Introduction to Strings and Branes |publisher=Cambridge University Press |date=2012 |isbn=978-0521817479 }}

* {{cite book |last1=Zwiebach |first1=Barton |title=A First Course in String Theory |date=2009 |publisher=Cambridge University Press |isbn=978-0-521-88032-9}}

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{{Commons category}}

{{Wikiquote}}

* [https://www.bbc.co.uk/science/horizon/2001/paralleluni.shtml bbc-horizon:BBC's parallel-uni''Parallel Universes'']—2002, 2002 feature documentary by ''[[Horizon (British TV series)|BBC Horizon]]'', episode "[[Parallel Universes (film)|Parallel Universes]]", focusfocuses on history and emergence of M-theory, and scientists involved.

; Websites :

* [https://www.pbs.org/wgbh/nova/physicsseries/the-elegant-universe.html/ pbs.org-nova:Nova's elegant-uni''The Elegant Universe'']—2003, 2003 [[Emmy Award]]-winning–winning, three-hour miniseries by ''[[Nova (American TV program)|Nova]]'' with [[Brian Greene]], adapted from his ''[[The Elegant Universe]]'' (original [[PBS]] broadcast dates: October 28, 8–10 p.m. and November 4, 8–9 p.m., 2003).

* [http://www.math.columbia.edu/~woit/blog/ Not Even Wrong]—A blog critical of string theory

* [https://whystringtheory.com/ Why String Theory]—An introduction to string theory.

* [https://www.quantumfieldtheory.info/String_Topics_Summaries.pdf Pedagogic Aids to String Theory]—Introductory level overview of string theory plus aids to help understanding some of the more difficult concepts. For those who have studied quantum field theory from the author of Student Friendly Quantum Field Theory.

; Video :

* [https://www.bbc.co.uk/science/horizon/2001/paralleluni.shtml bbc-horizon: parallel-uni]—2002 feature documentary by [[Horizon (British TV series)|BBC Horizon]], episode [[Parallel Universes (film)|Parallel Universes]] focus on history and emergence of M-theory, and scientists involved.

* [https://www.pbs.org/wgbh/nova/physics/elegant-universe.html pbs.org-nova: elegant-uni]—2003 [[Emmy Award]]-winning, three-hour miniseries by [[Nova (American TV program)|Nova]] with [[Brian Greene]], adapted from his [[The Elegant Universe]] (original [[PBS]] broadcast dates: October 28, 8–10 p.m. and November 4, 8–9 p.m., 2003).

{{String theory topics |state=collapsed}}

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{{Authority control}}

[[Category:String theory| ]]

[[Category:Concepts in physics]]

[[Category:Dimension]]

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[[Category:Multi-dimensional geometry]]

[[Category:Physics beyond the Standard Model]]

[[Category:String theory| ]]