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{{seeintroIntroduction to Mtheory}}

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{{String theorycTopic=Theory}} 

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In physics, '''string theory''' is a [[mathematical theorytheoretical framework]] in which the [[point particlepointlike particles]] of [[particle physics]] are replaced by [[one dimensionalonedimensional]] objects called [[string (physics)strings]].<ref name = DarkMatter>Sean Carroll, Ph.D., Cal Tech, 2007, The Teaching Company, ''Dark Matter, Dark Energy: The Dark Side of the Universe'', Guidebook Part 2 page 59, Accessed Oct. 7, 2013, "...The idea that the elementary constituents of matter are small loops of string rather than pointlike particles ... we think of string theory as a candidate theory of quantum gravity..."</ref> In string theory, the different types of observed [[elementary particle]]s arise from the different [[quantum state]]s of these strings. In addition to the types of particles postulated by the [[standard model of particle physics]], string theory naturally incorporates [[gravity]], and is therefore a candidate for a [[theory of everything]], a selfcontained [[mathematical model]] that describes all [[fundamental interactionfundamental forces]] and [[matterforms of matter]]. Aside from this hypothesized role in particle physics, string theory is now widely used as a theoretical tool in [[physics]], and it has shed light on many aspects of [[quantum field theory]] and [[quantum gravity]].<ref>{{cite journal author=Klebanov, Igor and Maldacena, Juan  title=Solving Quantum Field Theories via Curved Spacetimes journal=[[Physics Today]] year=2009  url=http://www.sns.ias.edu/~malda/Published.pdf format=PDF accessdate=May, 2013page=28 doi=10.1063/1.3074260 volume=62}}</ref> 

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The earliest version of string theory, called [[bosonic string theory]], incorporated only the class of [[particle]]s known as [[boson]]s, although this theory developed into [[superstring theory]], which posits that a connection (a "[[supersymmetry]]") exists between bosons and the class of particles called [[fermions]]. String theory requires the existence of extra [[spatial dimension]]s for its [[mathematical]] consistency. In realistic [[physical model]]s constructed from string theory, these extra dimensions are typically [[Compactification (physics)compactified]] to extremely small scales. 

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String theory was first studied in the late 1960s as a theory of the [[strong nuclear force]] before being abandoned in favor of the theory of [[quantum chromodynamics]]. Subsequently, it was realized that the very properties that made string theory unsuitable as a [[nuclear physicstheory of nuclear physics]] made it an outstanding candidate for a [[quantum theory of gravity]]. Five consistent versions of string theory were developed before it was realized in the mid1990s that these theories could be obtained as different limits of a conjectured elevendimensional theory called [[Mtheory]].<ref>{{cite journalauthor=Schwarz, John H. arxiv=hepth/9807135 title=From Superstrings to M Theorydoi=10.1016/S03701573(99)000162year=1999journal=Physics Reportsvolume=315pages=107bibcode = 1999PhR...315..107S }}</ref> 

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Many [[theoretical physicist]]s (among them [[Stephen Hawking]], [[Edward Witten]], and [[Juan Maldacena]]) believe that string theory is a step towards the correct [[fundamental researchfundamental description]] of [[physical propertiesnature]]. This is because string theory allows for the consistent combination of [[quantum field theory]] and [[general relativity]], agrees with general insights in [[quantum gravity]] such as the [[holographic principle]] and [[black hole thermodynamics]], and because it has passed many nontrivial checks of its internal consistency. According to Hawking in particular, "Mtheory is the ''only'' candidate for a complete theory of the universe."<ref>{{cite booklast=Hawkingfirst=Stephentitle=The Grand Designyear=2010publisher=Bantam Booksisbn=055338466X}}</ref> Other physicists, such as [[Richard Feynman]],<ref>{{Cite book first = Peter  last = Woit  authorlink = Peter Woit  year = 2006  title = Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law  publisher = New York: Basic Books  location = London: Jonathan Cape &  page=174  isbn = 0465092756 }}</ref><ref>P.C.W Davies and J. Brown (ed), "Superstrings, A Theory of Everything?", Cambridge University Press, 1988. ISBN 0521357411.</ref> [[Roger Penrose]],<ref>Penrose, Roger (2005). The Road to Reality: A Complete Guide to the Laws of the Universe. Knopf. ISBN 0679454438.</ref> and [[Sheldon Lee Glashow]],<ref>Sheldon Glashow. [http://www.pbs.org/wgbh/nova/elegant/viewglashow.html "NOVA – The elegant Universe"]. Pbs.org. Retrieved on 20120711.</ref> have criticized string theory for not providing novel experimental predictions at accessible [[energy scale]]s and say that it is a failure as a theory of everything. 

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== Overview == 

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[[File:String theory.svgrightthumb250pxLevels of magnification: <br />1. Macroscopic level: Matter <br />2. Molecular level <br />3. Atomic level: Protons, neutrons, and electrons <br />4. Subatomic level: Electron <br />5. Subatomic level: Quarks <br />6. String level]] 

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The starting point for string theory is the idea that the pointlike particles of elementary [[particle physics]] can also be modeled as onedimensional objects called ''strings''. According to string theory, strings can oscillate in many ways. On distance scales larger than the string radius, each oscillation mode gives rise to a different species of particle, with its [[mass]], [[charge (physics)charge]], and other properties determined by the string's dynamics. Splitting and recombination of strings correspond to particle emission and absorption, giving rise to the interactions between particles. An analogy for strings' modes of vibration is a guitar string's production of multiple distinct musical notes. In this analogy, different notes correspond to different particles. 

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In string theory, one of the modes of oscillation of the string corresponds to a massless, spin2 particle. Such a particle is called a [[graviton]] since it mediates a force which has the properties of [[gravity]]. Since string theory is believed to be a mathematically consistent quantum mechanical theory, the existence of this graviton state implies that string theory is a theory of [[quantum gravity]]. 

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String theory includes both ''open'' strings, which have two distinct endpoints, and ''closed'' strings, which form a complete loop. The two [[String (physics)#Types of stringstypes of string]] behave in slightly different ways, yielding different particle types. For example, all string theories have closed string [[graviton]] modes, but only open strings can correspond to the particles known as [[photons]]. Because the two ends of an open string can always meet and connect, forming a closed string, all string theories contain closed strings. 

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The earliest string model, the [[bosonic string theorybosonic string]], incorporated only the class of particles known as [[bosons]]. This model describes, at low enough energies, a [[quantum gravity]] theory, which also includes (if open strings are incorporated as well) [[gauge bosons]] such as the photon. However, this model has problems. What is most significant is that the theory has a fundamental instability, believed to result in the decay (at least partially) of spacetime itself. In addition, as the name implies, the spectrum of particles contains only bosons, particles which, like the photon, obey particular rules of behavior. Roughly speaking, bosons are the constituents of radiation, but not of matter, which is made of [[fermions]]. Investigating how a string theory may include fermions led to the invention of [[supersymmetry]], a mathematical relation between bosons and fermions. String theories that include fermionic vibrations are now known as [[superstring theorysuperstring theories]]; several kinds have been described, but all are now thought to be different limits of a theory called [[Mtheory]]. 

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Since string theory incorporates all of the fundamental interactions, including gravity, many physicists hope that 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 is quantitatively identical with the [[standard model]], with a small cosmological constant, containing [[dark matter]] and a plausible mechanism for [[cosmic inflation]]. It is not yet known whether string theory has such a solution, nor is it known how much freedom the theory allows to choose the details. 

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One of the challenges of string theory is that the full theory does not yet have a satisfactory definition in all circumstances. The scattering of strings is most straightforwardly defined using the techniques of [[perturbation theory (quantum mechanics)perturbation theory]], but it is not known in general how to define string theory [[Nonperturbativenonperturbatively]]. It is also not clear as to whether there is any principle by which string theory selects its [[vacuum state]], the spacetime configuration that determines the properties of our universe (see [[string theory landscape]]). 

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===Strings=== 

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The motion of a pointlike particle can be described by drawing a graph of its position with respect to time. The resulting picture depicts the [[worldline]] of the particle in [[spacetime]]. In an analogous way, one can draw a graph depicting the progress of a ''string'' as time passes. The string, which looks like a small line by itself, will sweep out a twodimensional surface known as the [[worldsheet]]. The different string modes (giving rise to different particles, such as the [[photon]] or [[graviton]]) appear as waves on this surface. 

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A [[String (physics)#Types of stringsclosed string]] looks like a small loop, so its worldsheet will look like a pipe. An open string looks like a segment with two endpoints, so its worldsheet will look like a strip. In a more mathematical language, these are both [[Riemann surfaces]], the strip having a boundary and the pipe none. 

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[[Image:World lines and world sheet.svgrightthumb300pxInteraction in the subatomic world: [[world line]]s of pointlike [[Subatomic particleparticles]] in the [[Standard Model]] or a [[world sheet]] swept up by closed [[string (physics)strings]] in string theory]] 

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Strings can join and split. This is reflected by the form of their worldsheet, or more precisely, by its [[topology]]. For example, if a closed string splits, its worldsheet will look like a single pipe splitting into two pipes. This topology is often referred to as a ''pair of pants'' (see drawing at right). If a closed string splits and its two parts later reconnect, its worldsheet will look like a single pipe splitting to two and then reconnecting, which also looks like a [[torus]] connected to two pipes (one representing the incoming string, and the other representing the outgoing one). An open string doing the same thing will have a worldsheet that looks like an [[Annulus (mathematics)annulus]] connected to two strips. 

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In [[quantum mechanics]], one computes the probability for a point particle to propagate from one point to another by summing certain quantities called [[probability amplitude]]s. Each amplitude is associated with a different worldline of the particle. This process of summing amplitudes over all possible worldlines is called [[Path integral formulationpath integration]]. In string theory, one computes probabilities in a similar way, by summing quantities associated with the worldsheets joining an initial string configuration to a final configuration. It is in this sense that string theory extends quantum field theory, replacing point particles by strings. As in quantum field theory, the classical behavior of fields is determined by an [[Action (physics)action functional]], which in string theory can be either the [[NambuGoto action]] or the [[Polyakov action]]. 

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===Branes=== 

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{{MainBraneDbrane}} 

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In string theory and related theories such as [[Supergravitysupergravity theories]], a ''brane'' is a physical object that generalizes the notion of a point particle to higher dimensions.<ref>{{cite journal author=Moore, Gregory  title=What is... a Brane? journal=Notices of the AMS year=2005  url=http://www.ams.org/notices/200502/whatis.pdf format=PDF accessdate=June, 2013 page=214 volume=52}}</ref> For example, a point particle can be viewed as a brane of dimension zero, while a string can be viewed as a brane of dimension one. It is also possible to consider higher dimensional branes. In dimension ''p'', these are called ''p''branes. The word brane comes from the word "membrane" which refers to a twodimensional brane. 

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Branes are dynamical objects which can propagate through spacetime according to the rules of [[quantum mechanics]]. They have mass and can have other attributes such as [[Charge (physics)charge]]. A ''p''brane sweeps out a (''p''+1)dimensional volume in spacetime called its ''worldvolume''. Physicists often study fields analogous to the [[electromagnetic field]] which live on the worldvolume of a brane. 

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In string theory, Dbranes are an important class of branes that arise when one considers open strings. As an open string propagates through spacetime, its endpoints are required to lie on a Dbrane. The letter "D" in Dbrane refers to the fact that we impose a certain mathematical condition on the system known as the [[Dirichlet boundary condition]]. The study of Dbranes in string theory has led to important results such as the [[AdS/CFT correspondence]], which has shed light on many problems in quantum field theory. 

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Branes are also frequently studied from a [[Pure mathematicspurely mathematical]] point of view<ref> 

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{{cite book editor1first=Paul editor1last=Aspinwall editor2first=Tom editor2last=Bridgeland editor3first=Alastair editor3last=Craw editor4first=Michael editor4last=Douglas editor5first=Mark editor5last=Gross editor6first=Anton editor6last=Kapustin editor7first=Gregory editor7last=Moore editor8first=Graeme editor8last=Segal editor9first=Balázs editor9last=Szendröi editor10first=P.M.H. editor10last=Wilson title=Dirichlet Branes and Mirror Symmetry year=2009 publisher=American Mathematical Society}}</ref> since they are related to subjects such as [[homological mirror symmetry]] and [[noncommutative geometry]]. Mathematically, branes may be represented as objects of certain [[Category (mathematics)categories]], such as the [[derived category]] of [[Coherent sheafcoherent sheaves]] on a [[CalabiYau manifold]], or the [[Fukaya category]]. 

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===Dualities=== 

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In physics, the term ''duality'' refers to a situation where two seemingly different [[physical system]]s turn out to be equivalent in a nontrivial way. If two theories are related by a duality, it means that one theory can be transformed in some way so that it ends up looking just like the other theory. The two theories are then said to be ''dual'' to one another under the transformation. Put differently, the two theories are mathematically different descriptions of the same phenomena. 

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In addition to providing a candidate for a [[theory of everything]], string theory provides many examples of dualities between different physical theories and can therefore be used as a tool for understanding the relationships between these theories.<ref>{{nlabid=duality+in+string+theorytitle=Duality in string theory}}</ref> 

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====S, T, and Uduality==== 

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{{MainSdualityTdualityUduality}} 

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These are dualities between string theories which relate seemingly different quantities. Large and small distance scales, as well as strong and weak coupling strengths, are quantities that have always marked very distinct limits of behavior of a physical system in both [[Classical physicsclassical]] and [[quantum physics]]. But strings can obscure the difference between large and small, strong and weak, and this is how these five very different theories end up being related. Tduality relates the large and small distance scales between string theories, whereas Sduality relates strong and weak coupling strengths between string theories. Uduality links Tduality and Sduality. 

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====Mtheory==== 

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{{MainMtheory}} 

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Before the 1990s, string theorists believed there were five distinct superstring theories: [[type I stringtype I]], [[type IIA stringtype IIA]], [[type IIB stringtype IIB]], and the two flavors of [[heterotic string]] theory ([[special orthogonal groupSO(32)]] and [[E8 (mathematics)''E''<sub>8</sub>×''E''<sub>8</sub>]]). The thinking was that out of these five candidate theories, only one was the actual correct [[theory of everything]], and that theory was the one whose low energy limit, with ten spacetime dimensions [[compactification (physics)compactified]] down to four, matched the physics observed in our world today. It is now believed that this picture was incorrect and that the five superstring theories are related to one another by the dualities described above. The existence of these dualities suggests that the five string theories are in fact special cases of some more fundamental theory called [[Mtheory]].<ref>{{cite journal last1=Witten first1=Edward year=1995 title=String theory dynamics in various dimensions journal=Nuclear Physics B volume=443 issue=1 pages=85–126 doi=10.1016/05503213(95)00158Oarxiv = hepth/9503124 bibcode = 1995NuPhB.443...85W }}</ref> 

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{ class="wikitable" 

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+ String theory details by type and number of spacetime dimensions 

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! scope="col"  Type 

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! scope="col"  Spacetime dimensions 

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! scope="col"  Details 

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! scope="row"  Bosonic 

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 style="textalign: center;"  26  Only [[boson]]s, no [[fermion]]s, meaning only forces, no matter, with both open and closed strings; major flaw: a [[particle physicsparticle]] with imaginary mass, called the [[tachyon]], representing an instability in the theory. 

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! scope="row"  I 

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 style="textalign: center;"  10  [[Supersymmetry]] between forces and matter, with both open and closed strings; no tachyon; group symmetry is [[special orthogonal groupSO(32)]] 

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! scope="row"  IIA 

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 style="textalign: center;"  10  Supersymmetry between forces and matter, with only closed strings bound to [[Dbrane]]s; no tachyon; massless [[fermion]]s are non[[chirality (physics)chiral]] 

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! scope="row"  IIB 

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 style="textalign: center;"  10  Supersymmetry between forces and matter, with only closed strings bound to Dbranes; no tachyon; massless fermions are chiral 

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! scope="row"  HO 

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 style="textalign: center;"  10  Supersymmetry between forces and matter, with closed strings only; no tachyon; [[Heterotic string theoryheterotic]], meaning right moving and left moving strings differ; group symmetry is [[special orthogonal groupSO(32)]] 

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! scope="row"  HE 

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 style="textalign: center;"  10  Supersymmetry between forces and matter, with closed strings only; no tachyon; heterotic; group symmetry is [[E8 (mathematics)''E''<sub>8</sub>×''E''<sub>8</sub>]] 

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} 

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===Extra dimensions=== 

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====Number of dimensions==== 

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An intriguing feature of string theory is that it predicts extra dimensions. In classical string theory the number of dimensions is not fixed by any consistency criterion. However, to make a consistent quantum theory, string theory is required to live in a spacetime of the socalled "[[critical dimension]]": we must have 26 spacetime dimensions for the [[bosonic string]] and 10 for the [[superstring]]. This is necessary to ensure the vanishing of the [[conformal anomaly]] of the worldsheet [[conformal field theory]]. Modern understanding indicates that there exist less trivial ways of satisfying this criterion. Cosmological solutions exist in a wider variety of dimensionalities, and these different dimensions are related by dynamical transitions. The dimensions are more precisely different values of the "effective central charge", a count of degrees of freedom that reduces to dimensionality in weakly curved regimes.<ref>{{cite journaldoi=10.1088/11266708/2007/09/096arxiv=hepth/0612051v3title=Dimensionchanging exact solutions of string theoryyear=2007last1=Hellermanfirst1=Simeonlast2=Swansonfirst2=Ianjournal=Journal of High Energy Physicsvolume=2007issue=9pages=096bibcode = 2007JHEP...09..096H }}</ref><ref>{{cite journaldoi=10.1103/PhysRevD.75.046003arxiv=hepth/0612031v2title=Supercritical stability, transitions, and (pseudo)tachyonsyear=2007last1=Aharonyfirst1=Oferlast2=Silversteinfirst2=Evajournal=Physical Review Dvolume=75issue=4bibcode = 2007PhRvD..75d6003A }}</ref> 

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One such theory is the 11dimensional [[Mtheory]], which requires [[spacetime]] to have eleven dimensions,<ref name="arxiv2">{{cite journalauthor=Duff, M. J.; Liu, James T. and Minasian, R. arxiv=hepth/9506126v2 title=Eleven Dimensional Origin of String/String Duality: A One Loop Testdoi=10.1016/05503213(95)003683year=1995journal=Nuclear Physics Bvolume=452pages=261bibcode = 1995NuPhB.452..261D }}</ref> as opposed to the usual three spatial dimensions and the fourth dimension of time. The original string theories from the 1980s describe special cases of Mtheory where the eleventh dimension is a very small circle or a line, and if these formulations are considered as fundamental, then string theory requires ten dimensions. But the theory also describes universes like ours, with four observable spacetime dimensions, as well as universes with up to 10 flat space dimensions, and also cases where the position in some of the dimensions is described by a [[complex number]] rather than a real number. The notion of spacetime dimension is not fixed in string theory: it is best thought of as different in different circumstances.<ref name=Polchinski>Polchinski, Joseph (1998). ''String Theory'', Cambridge University Press ISBN 0521672295.</ref> 

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Nothing in [[James Clerk MaxwellMaxwell]]'s theory of [[electromagnetism]] or [[Albert EinsteinEinstein]]'s [[theory of relativity]] makes this kind of prediction; these theories require physicists to insert the number of dimensions manually and arbitrarily, and this number is fixed and independent of potential energy. String theory allows one to relate the number of dimensions to scalar potential energy. In technical terms, this happens because a [[gauge anomaly]] exists for every separate number of predicted dimensions, and the gauge anomaly can be counteracted by including nontrivial potential energy into equations to solve motion. Furthermore, the absence of potential energy in the "critical dimension" explains why flat spacetime solutions are possible. 

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This can be better understood by noting that a [[photon]] included in a consistent theory (technically, a particle carrying a force related to an unbroken [[gauge symmetry]]) must be [[rest massmassless]]. The mass of the photon that is predicted by string theory depends on the energy of the string mode that represents the photon. This energy includes a contribution from the [[Casimir effect]], namely from [[quantum fluctuation]]s in the string. The size of this contribution depends on the number of dimensions, since for a larger number of dimensions there are more possible fluctuations in the string position. Therefore, the photon in flat spacetime will be massless—and the theory consistent—only for a particular number of dimensions.<ref>The calculation of the number of dimensions can be circumvented by adding a [[degrees of freedom (physics and chemistry)degree of freedom]], which compensates for the "missing" quantum fluctuations. However, this degree of freedom behaves similar to [[spacetime]] dimensions only in some aspects, and the produced theory is not [[Lorentz invariant]], and has other characteristics that do not appear in nature. This is known as the ''[[linear dilaton]]'' or [[noncritical string]].</ref> 

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When the calculation is done, the critical dimensionality is not four as one may expect (three axes of space and one of time). 

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The subset of X is equal to the relation of photon fluctuations in a linear dimension. Flat space string theories are 26dimensional in the bosonic case, while superstring and Mtheories turn out to involve 10 or 11 dimensions for flat solutions. In bosonic string theories, the 26 dimensions come from the Polyakov equation.<ref>Botelho, Luiz C. L. and Botelho, Raimundo C. L. (1999) [http://cds.cern.ch/record/405669 "Quantum Geometry of Bosonic Strings – Revisited"]. Centro Brasileiro de Pesquisas Físicas.</ref> Starting from any dimension greater than four, it is necessary to consider how these are reduced to four dimensional [[spacetime]]. 

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====Compact dimensions==== 

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[[Image:CalabiYau.pngrightthumb200px[[Calabi–Yau manifold]] ([[3D projection]])]] 

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Two ways have been proposed to resolve this apparent contradiction. The first is to [[Compactification (physics)compactify]] the extra dimensions; i.e., the 6 or 7 extra dimensions are so small as to be undetectable by presentday experiments. 

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To retain a high degree of supersymmetry, these compactification spaces must be very special, as reflected in their [[holonomy]]. A 6dimensional manifold must have SU(3) structure, a particular case ([[torsion tensortorsionless]]) of this being SU(3) holonomy, making it a [[Calabi–Yau space]], and a 7dimensional manifold must have [[G2 manifoldG<sub>2</sub>]] structure, with G<sub>2</sub> holonomy again being a specific, simple, case. Such spaces have been studied in attempts to relate string theory to the 4dimensional [[Standard Model]], in part due to the computational simplicity afforded by the assumption of supersymmetry. More recently, progress has been made constructing more realistic compactifications without the degree of symmetry of Calabi–Yau or G2 manifolds.{{Citation neededdate=November 2012}} 

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A standard analogy for this is to consider multidimensional space as a garden hose. If the hose is viewed from sufficient distance, it appears to have only one dimension, its length. Indeed, think of a ball just small enough to enter the hose. Throwing such a ball inside the hose, the ball would move more or less in one dimension; in any experiment we make by throwing such balls in the hose, the only important movement will be onedimensional, that is, along the hose. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling inside it would move in two dimensions (and a fly flying in it would move in three dimensions). This "extra dimension" is only visible within a relatively close range to the hose, or if one "throws in" small enough objects. Similarly, the extra compact dimensions are only "visible" at extremely small distances, or by experimenting with particles with extremely small [[wavelength]]s (of the order of the compact dimension's radius), which in [[quantum mechanics]] means very high energies (see [[waveparticle duality]]). 

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====Braneworld scenario==== 

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Another possibility is that we are "stuck" in a 3+1 dimensional (three spatial dimensions plus one time dimension) subspace of the full universe. Properly localized matter and Yang–Mills gauge fields will typically exist if the subspacetime is an exceptional set of the larger universe.<ref>{{cite journalauthor=Hübsch, T.url=https://web.archive.org/web/20101207045114/http://homepage.mac.com/thubsch/HSProc.pdf title=A Hitchhiker's Guide to Superstring Jump Gates and Other Worldsdoi=10.1016/S09205632(96)005890year=1997journal=Nuclear Physics B – Proceedings Supplementsvolume=52pages=347bibcode = 1997NuPhS..52..347H }}</ref> These "exceptional sets" are ubiquitous in Calabi–Yau ''n''folds and may be described as subspaces without local deformations, akin to a crease in a sheet of paper or a crack in a crystal, the neighborhood of which is markedly different from the exceptional subspace itself. However, until the work of Randall and Sundrum,<ref> 

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{{cite journaldoi=10.1103/PhysRevLett.83.4690arxiv=hepth/9906064title=An Alternative to Compactificationyear=1999last1=Randallfirst1=Lisajournal=Physical Review Lettersvolume=83issue=23pages=4690bibcode = 1999PhRvL..83.4690R }}</ref> it was not known that gravity can be properly localized to a subspacetime. In addition, spacetime may be stratified, containing strata of various dimensions, allowing us to inhabit the 3+1dimensional stratum—such geometries occur naturally in Calabi–Yau compactifications.<ref> 

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{{cite journaldoi=10.1016/05503213(94)903212arxiv=hepth/9309097title=CalabiYau moduli space, mirror manifolds and spacetime topology change in string theoryyear=1994last1=Aspinwallfirst1=Paul S.last2=Greenefirst2=Brian R.last3=Morrisonfirst3=David R.journal=Nuclear Physics Bvolume=416issue=2pages=414bibcode = 1994NuPhB.416..414A }}</ref> Such subspacetimes are [[Dbrane]]s, hence such models are known as [[brane cosmologybraneworld]] scenarios. 

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====Effect of the hidden dimensions==== 

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In either case, gravity acting in the hidden dimensions affects other nongravitational forces such as electromagnetism. In fact, Kaluza's early work demonstrated that general relativity in five dimensions actually predicts the existence of electromagnetism. However, because of the nature of [[Calabi–Yau manifold]]s, no new forces appear from the small dimensions, but their shape has a profound effect on how the forces between the strings appear in our fourdimensional universe. In principle, therefore, it is possible to deduce the nature of those extra dimensions by requiring consistency with the [[standard model]], but this is not yet a practical possibility. It is also possible to extract information regarding the hidden dimensions by precision tests of gravity, but so far these have only put upper limitations on the size of such hidden dimensions. 

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==Testability and experimental predictions== 

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Although a great deal of recent work has focused on using string theory to construct realistic models of [[particle physics]], several major difficulties complicate efforts to test models based on string theory. The most significant is the extremely small size of the [[Planck length]], which is expected to be close to the string length (the characteristic size of a string, where strings become easily distinguishable from particles). Another issue is the huge number of metastable vacua of string theory, which might be sufficiently diverse to accommodate almost any phenomena we might observe at lower energies. 

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===String harmonics=== 

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One unique prediction of string theory is the existence of ''string harmonics''. At sufficiently high energies, the stringlike nature of particles would become obvious. There should be heavier copies of all particles, corresponding to higher vibrational harmonics of the string. It is not clear how high these energies are. In most conventional string models, they would be close to the [[Planck energy]], which is 10<sup>14</sup> times higher than the energies accessible in the newest [[particle accelerator]], the [[Large Hadron ColliderLHC]], making this prediction impossible to test with any particle accelerator in the near future. However, in models with [[large extra dimensions]] they could potentially be produced at the LHC, or at energies not far above its reach. 

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===Cosmology=== 

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String theory as currently understood makes a series of predictions for the structure of the universe at the largest scales. Many phases in string theory have very large, positive [[vacuum energy]].<ref name="KKLT" /> Regions of the universe that are in such a phase will inflate exponentially rapidly in a process known as [[eternal inflation]]. As such, the theory predicts that most of the universe is very rapidly expanding. However, these expanding phases are not stable, and can decay via the nucleation of bubbles of lower vacuum energy. Since our local region of the universe is not very rapidly expanding, string theory predicts we are inside such a bubble. The [[spatial curvature]] of the "universe" inside the bubbles that form by this process is negative, a testable prediction.<ref name = "obscon">{{cite journaldoi=10.1088/11266708/2006/03/039arxiv=hepth/0505232title=Observational consequences of a landscapeyear=2006last1=Freivogelfirst1=Benlast2=Klebanfirst2=Matthewlast3=Martínezfirst3=María Rodríguezlast4=Susskindfirst4=Leonardjournal=Journal of High Energy Physicsvolume=2006issue=3pages=039bibcode = 2006JHEP...03..039F }}</ref> Moreover, other bubbles will eventually form in the parent vacuum outside the bubble and collide with it. These collisions lead to potentially observable imprints on cosmology.<ref name = "wakes">{{cite journalarxiv=1109.3473doi=10.1103/PhysRevD.87.041301title=Observing the multiverse with cosmic wakesyear=2013last1=Klebanfirst1=Matthewlast2=Levifirst2=Thomas S.last3=Sigurdsonfirst3=Krisjournal=Physical Review Dvolume=87issue=4bibcode = 2013PhRvD..87d1301K }}</ref> However, it is possible that neither of these will be observed if the spatial curvature is too small and the collisions are too rare. 

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Under certain circumstances, fundamental strings produced at or near the end of [[Inflation (cosmology)inflation]] can be "stretched" to astronomical proportions. These [[cosmic strings]] could be observed in various ways, for instance by their [[gravitational lensing]] effects. However, certain field theories also predict cosmic strings arising from topological defects in the field configuration.<ref>{{cite arXiveprint=hepth/0412244 title=Introduction to Cosmic F and DStrings first=Joseph last=Polchinskiclass=hepthyear=2004}}</ref> 

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===Supersymmetry=== 

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{{MainSupersymmetry}} 

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If confirmed experimentally, [[supersymmetry]] could also be considered circumstantial evidence, because all consistent string theories are supersymmetric. However, the absence of supersymmetric particles at energies accessible to the [[LHC]] would not necessarily disprove string theory, since the energy scale at which supersymmetry is broken could be well above the accelerator's range. 

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==AdS/CFT correspondence==<! This section is linked from String theory > 

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{{MainAdS/CFT correspondence}} 

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The antide Sitter/conformal field theory (AdS/CFT) correspondence is a relationship which says that string theory is in certain cases equivalent to a [[quantum field theory]]. More precisely, one considers string or Mtheory on an [[Antide Sitter spaceantide Sitter]] background. This means that the geometry of [[spacetime]] is obtained by perturbing a certain solution of [[Einstein's equation]] in the vacuum. In this setting, it is possible to define a notion of "boundary" of spacetime. The AdS/CFT correspondence states that this boundary can be regarded as the "spacetime" for a quantum field theory, and this field theory is equivalent to the bulk gravitational theory in the sense that there is a "dictionary" for translating calculations in one theory into calculations in the other. 

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===Examples of the correspondence=== 

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The most famous example of the AdS/CFT correspondence states that Type IIB string theory on the product '''AdS'''<sub>5</sub> × '''S'''<sup>5</sup> is equivalent to [[N = 4 super Yang–Mills''N'' = 4 super Yang–Mills theory]] on the fourdimensional conformal boundary.<ref>Maldacena, J. ''The Large N Limit of Superconformal Field Theories and Supergravity'', [[arXiv:hepth/9711200]]</ref><ref>{{cite journal  author=Gubser, S. S.; Klebanov, I. R. and Polyakov, A. M.  title=Gauge theory correlators from noncritical string theory  journal=Physics Letters  volume=B428  year=1998  pages=105–114  arxiv=hepth/9802109bibcode = 1998PhLB..428..105G doi = 10.1016/S03702693(98)003773 }}</ref><ref>{{cite journal  author=Edward Witten  title=Antide Sitter space and holography  journal=Advances in Theoretical and Mathematical Physics  volume=2  year=1998  pages=253–291  arxiv=hepth/9802150bibcode = 1998hep.th....2150W }}</ref><ref>{{cite journal title=Large N Field Theories, String Theory and Gravity first=O. last= Aharony coauthors= S.S. Gubser, J. Maldacena, H. Ooguri, Y. Oz journal= Phys. Rept. volume=323 issue=3–4 year=2000 pages= 183–386 arxiv=hepth/9905111 doi=10.1016/S03701573(99)000836 bibcode = 1999PhR...323..183A }}</ref> Another realization of the correspondence states that Mtheory on '''AdS'''<sub>4</sub> × '''S'''<sup>7</sup> is equivalent to the ABJM superconformal field theory in three dimensions.<ref>{{cite journalarxiv=0806.1218 title=''N'' = 6 superconformal ChernSimonsmatter theories, M2branes and their gravity dualsdoi=10.1088/11266708/2008/10/091year=2008last1=Aharonyfirst1=Oferlast2=Bergmanfirst2=Orenlast3=Jafferisfirst3=Daniel Louislast4=Maldacenafirst4=Juanjournal=Journal of High Energy Physicsvolume=2008issue=10pages=091bibcode = 2008JHEP...10..091A }}</ref> Yet another realization states that Mtheory on '''AdS'''<sub>7</sub> × '''S'''<sup>4</sup>is equivalent to the socalled (2,0)theory in six dimensions.<ref>{{nlabid=6d+%282%2C0%29supersymmetric+QFTtitle=6d (2,0)supersymmetric QFT}}</ref> 

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===Applications to quantum chromodynamics=== 

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{{MainAdS/QCD}} 

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Since it relates string theory to ordinary quantum field theory, the AdS/CFT correspondence can be used as a theoretical tool for doing calculations in quantum field theory. For example, the correspondence has been used to study the [[quarkgluon plasma]], an exotic state of matter produced in particle accelerators. 

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The physics of the quarkgluon plasma is governed by [[quantum chromodynamics]], the fundamental theory of the [[strong interactionstrong nuclear force]], but this theory is mathematically intractable in problems involving the quarkgluon plasma. In order to understand certain properties of the quarkgluon plasma, theorists have therefore made use of the AdS/CFT correspondence. One version of this correspondence relates string theory to a certain [[supersymmetric gauge theory]] called [[N = 4 super Yang–Mills''N'' = 4 super Yang–Mills theory]]. The latter theory provides a good approximation to [[quantum chromodynamics]]. One can thus translate problems involving the quarkgluon plasma into problems in string theory which are more tractable. Using these methods, theorists have computed the shear viscosity of the quarkgluon plasma.<ref>{{cite journal  last1 = Kovtun  first1 = P. K.  last2 = Son  first2 = Dam T.  last3 = Starinets  first3 = A. O.  title = Viscosity in strongly interacting quantum field theories from black hole physics  journal = Physical review letters  volume = 94  issue = 11  year = 2001}}</ref> In 2008, these predictions were confirmed at the [[Relativistic Heavy Ion Collider]] at [[Brookhaven National Laboratory]].<ref>{{cite journal  last1 = Luzum  first1 = Matthew  last2 = Romatschke  first2 = Paul  title = Conformal relativistic viscous hydrodynamics: Applications to RHIC results at sqrt [s_ {NN}]= 200 GeV  journal = Physical Review C  volume = 78  issue = 3  year = 2008arxiv=0804.4015doi=10.1103/PhysRevC.78.034915bibcode = 2008PhRvC..78c4915L }}</ref> 

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===Applications to condensed matter physics=== 

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In addition, string theory methods have been applied to problems in [[condensed matter physics]]. Certain condensed matter systems are difficult to understand using the usual methods of quantum field theory, and the AdS/CFT correspondence may allow physicists to better understand these systems by describing them in the language of string theory. Some success has been achieved in using string theory methods to describe the transition of a [[superfluid]] to an [[insulator (electricity)insulator]].<ref>{{cite journal  last1 = Merali  first1 = Zeeya  title = Collaborative physics: string theory finds a bench mate  journal = Nature  volume = 478  pages = 302–304  year = 2011  doi = 10.1038/478302a  pmid = 22012369  issue = 7369bibcode = 2011Natur.478..302M }}</ref><ref>{{cite journal  last1 = Sachdev  first1 = Subir  title = Strange and stringy  journal = Scientific American  volume = 308  issue = 44  year = 2013doi=10.1038/scientificamerican011344  pages = 44bibcode = 2012SciAm.308a..44S }}</ref> 

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==Connections to mathematics== 

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In addition to influencing research in [[theoretical physics]], string theory has stimulated a number of major developments in [[pure mathematics]]. Like many developing ideas in theoretical physics, string theory does not at present have a [[mathematical rigormathematically rigorous]] formulation in which all of its concepts can be defined precisely. As a result, physicists who study string theory are often guided by physical intuition to conjecture relationships between the seemingly different mathematical structures that are used to formalize different parts of the theory. These conjectures are later proved by mathematicians, and in this way, string theory has served as a source of new ideas in pure mathematics.<ref> 

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{{cite book editor1first=Pierre editor1last=Deligne editor2first=Pavel editor2last=Etingof editor3first=Daniel editor3last=Freed editor4first=Lisa editor4last=Jeffery editor5first=David editor5last=Kazhdan editor6first=John editor6last=Morgan editor7first=David editor7last=Morrison editor8first=Edward editor8last=Witten title=Quantum Fields and Strings: A Course for Mathematicians volume=1 year=1999 publisher=American Mathematical Society page=1isbn=0821820125}}</ref> 

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===Mirror symmetry=== 

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{{MainMirror symmetry (string theory)}} 

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One of the ways in which string theory influenced mathematics was through the discovery of [[mirror symmetry (string theory)mirror symmetry]]. In string theory, the shape of the unobserved spatial dimensions is typically encoded in mathematical objects called [[CalabiYau manifold]]s. These are of interest in pure mathematics, and they can be used to construct realistic models of physics from string theory. In the late 1980s, it was noticed that given such a physical model, it is not possible to uniquely reconstruct a corresponding CalabiYau manifold. Instead, one finds that there are ''two'' CalabiYau manifolds that give rise to the same physics. These manifolds are said to be "mirror" to one another. The existence of this mirror symmetry relationship between different CalabiYau manifolds has significant mathematical consequences as it allows mathematicians to solve many problems in [[enumerative geometryenumerative algebraic geometry]]. Today mathematicians are still working to develop a mathematical understanding of mirror symmetry based on physicists' intuition.<ref> 

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{{cite book editor1first=Kentaro editor1last=Hori editor2first=Sheldon editor2last=Katz editor3first=Albrecht editor3last=Klemm editor4first=Rahul editor4last=Pandharipande editor5first=Richard editor5last=Thomas editor6first=Cumrun editor6last=Vafa editor7first=Ravi editor7last=Vakil editor8first=Eric editor8last= Zaslowtitle=Mirror Symmetry year=2003 publisher=American Mathematical Societyurl=http://math.stanford.edu/~vakil/files/mirrorfinal.pdfisbn=0821829556}}</ref> 

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===Vertex operator algebras=== 

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{{MainVertex operator algebraMonstrous moonshine}} 

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In addition to mirror symmetry, applications of string theory to pure mathematics include results in the theory of [[vertex operator algebra]]s. For example, ideas from string theory were used by [[Richard Borcherds]] in 1992 to prove the [[monstrous moonshine]] conjecture relating the [[monster group]] (a construction arising in [[group theory]], a branch of algebra) and [[modular function]]s (a class of functions which are important in [[number theory]]).<ref>{{cite book last1=Frenkel first1=Igor last2=Lepowsky first2=James last3=Meurman first3=Arne title=Vertex operator algebras and the Monster series=Pure and Applied Mathematics volume=134 year=1988 publisher=Academic Press location=Boston isbn= 0122670655}}</ref> 

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==History== 

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{{unreferenced sectiondate=February 2013}} 

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{{MainHistory of string theory}} 

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===Early results=== 

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Some of the structures reintroduced by string theory arose for the first time much earlier as part of the program of classical unification started by [[Albert Einstein]]. The first person to add a [[Fivedimensional spacefifth dimension]] to [[general relativity]] was German mathematician [[Theodor Kaluza]] in 1919, who noted that gravity in five dimensions describes both gravity and electromagnetism in four. In 1926, the Swedish physicist [[Oskar Klein]] gave [[KaluzaKlein theorya physical interpretation]] of the unobservable extra dimension—it is wrapped into a small circle. Einstein introduced a [[Antisymmetric tensornonsymmetric]] [[metric tensor]], while much later Brans and Dicke added a scalar component to gravity. These ideas would be revived within string theory, where they are demanded by consistency conditions. 

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String theory was originally developed during the late 1960s and early 1970s as a never completely successful theory of [[hadron]]s, the [[subatomic particle]]s like the [[proton]] and [[neutron]] that feel the [[strong interaction]]. In the 1960s, [[Geoffrey Chew]] and [[Steven Frautschi]] discovered that the [[meson]]s make families called [[Regge trajectories]] with masses related to spins in a way that was later understood by [[Yoichiro Nambu]], [[Holger Bech Nielsen]] and [[Leonard Susskind]] to be the relationship expected from rotating strings. Chew advocated making a theory for the interactions of these trajectories that did not presume that they were composed of any fundamental particles, but would construct their interactions from [[bootstrap modelselfconsistency conditions]] on the [[Smatrix]]. The [[Smatrix theorySmatrix approach]] was started by [[Werner Heisenberg]] in the 1940s as a way of constructing a theory that did not rely on the local notions of space and time, which Heisenberg believed break down at the nuclear scale. While the scale was off by many orders of magnitude, the approach he advocated was ideally suited for a theory of quantum gravity. 

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Working with experimental data, R. Dolen, D. Horn and C. Schmid<ref> 

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{{cite journaldoi=10.1103/PhysRev.166.1768title=FiniteEnergy Sum Rules and Their Application to πN Charge Exchangeyear=1968last1=Dolenfirst1=R.last2=Hornfirst2=D.last3=Schmidfirst3=C.journal=Physical Reviewvolume=166issue=5pages=1768bibcode = 1968PhRv..166.1768D }}</ref> developed some sum rules for hadron exchange. When a particle and antiparticle scatter, virtual particles can be exchanged in two qualitatively different ways. In the schannel, the two particles annihilate to make temporary intermediate states that fall apart into the final state particles. In the tchannel, the particles exchange intermediate states by emission and absorption. In field theory, the two contributions add together, one giving a continuous background contribution, the other giving peaks at certain energies. In the data, it was clear that the peaks were stealing from the background—the authors interpreted this as saying that the tchannel contribution was dual to the schannel one, meaning both described the whole amplitude and included the other. 

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The result was widely advertised by [[Murray GellMann]], leading [[Gabriele Veneziano]] to construct a scattering amplitude that had the property of DolenHornSchmid duality, later renamed worldsheet duality. The amplitude needed poles where the particles appear, on straight line trajectories, and there is a special mathematical function whose poles are evenly spaced on half the real line— the [[Gamma function]]— which was widely used in Regge theory. By manipulating combinations of Gamma functions, Veneziano was able to find a consistent scattering amplitude with poles on straight lines, with mostly positive residues, which obeyed duality and had the appropriate Regge scaling at high energy. The amplitude could fit nearbeam scattering data as well as other Regge type fits, and had a suggestive integral representation that could be used for generalization. 

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Over the next years, hundreds of physicists worked to complete the [[Bootstrap modelbootstrap program]] for this model, with many surprises. Veneziano himself discovered that for the scattering amplitude to describe the scattering of a particle that appears in the theory, an obvious selfconsistency condition, the lightest particle must be a [[tachyon]]. [[Miguel Ángel Virasoro (physicist)Miguel Virasoro]] and Joel Shapiro found a different amplitude now understood to be that of closed strings, while [[Ziro Koba]] and [[Holger Bech NielsenHolger Nielsen]] generalized Veneziano's integral representation to multiparticle scattering. Veneziano and [[Sergio Fubini]] introduced an operator formalism for computing the scattering amplitudes that was a forerunner of worldsheet conformal theory, while Virasoro understood how to remove the poles with wrongsign residues using a constraint on the states. [[Claud Lovelace]] calculated a loop amplitude, and noted that there is an inconsistency unless the dimension of the theory is 26. [[Charles Thorn]], [[Peter Goddard (physicist)Peter Goddard]] and [[Richard Brower]] went on to prove that there are no wrongsign propagating states in dimensions less than or equal to 26. 

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In 1969, [[Yoichiro Nambu]], [[Holger Bech Nielsen]], and [[Leonard Susskind]] recognized that the theory could be given a description in space and time in terms of strings. The scattering amplitudes were derived systematically from the action principle by [[Peter Goddard (physicist)Peter Goddard]], [[Jeffrey Goldstone]], [[Claudio Rebbi]], and [[Charles Thorn]], giving a spacetime picture to the vertex operators introduced by Veneziano and Fubini and a geometrical interpretation to the [[Virasoro algebraVirasoro conditions]]. 

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In 1970, [[Pierre Ramond]] added fermions to the model, which led him to formulate a twodimensional supersymmetry to cancel the wrongsign states. [[John Henry SchwarzJohn Schwarz]] and [[André Neveu]] added another sector to the fermi theory a short time later. In the fermion theories, the critical dimension was 10. [[Stanley Mandelstam]] formulated a world sheet conformal theory for both the bose and fermi case, giving a twodimensional field theoretic pathintegral to generate the operator formalism. [[Michio Kaku]] and [[Keiji Kikkawa]] gave a different formulation of the bosonic string, as a [[string field theory]], with infinitely many particle types and with fields taking values not on points, but on loops and curves. 

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In 1974, [[Tamiaki Yoneya]] discovered that all the known string theories included a massless spintwo particle that obeyed the correct [[Ward identities]] to be a graviton. John Schwarz and [[Joel Scherk]] came to the same conclusion and made the bold leap to suggest that string theory was a theory of gravity, not a theory of hadrons. They reintroduced [[Kaluza–Klein theory]] as a way of making sense of the extra dimensions. At the same time, [[quantum chromodynamics]] was recognized as the correct theory of hadrons, shifting the attention of physicists and apparently leaving the bootstrap program in the [[dustbin of history]]. 

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String theory eventually made it out of the dustbin, but for the following decade all work on the theory was completely ignored. Still, the theory continued to develop at a steady pace thanks to the work of a handful of devotees. [[Ferdinando Gliozzi]], Joel Scherk, and [[David Olive]] realized in 1976 that the original Ramond and Neveu Schwarzstrings were separately inconsistent and needed to be combined. The resulting theory did not have a tachyon, and was proven to have spacetime supersymmetry by John Schwarz and [[Michael Green (physicist)Michael Green]] in 1981. The same year, [[Alexander Markovich PolyakovAlexander Polyakov]] gave the theory a modern path integral formulation, and went on to develop conformal field theory extensively. In 1979, [[Daniel Friedan]] showed that the equations of motions of string theory, which are generalizations of the [[Einstein equations]] of [[General Relativity]], emerge from the [[Renormalization group]] equations for the twodimensional field theory. Schwarz and Green discovered Tduality, and constructed two superstring theories—IIA and IIB related by Tduality, and type I theories with open strings. The consistency conditions had been so strong, that the entire theory was nearly uniquely determined, with only a few discrete choices. 

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===First superstring revolution=== 

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In the early 1980s, [[Edward Witten]] discovered that most theories of quantum gravity could not accommodate [[chirality (physics)chiral]] fermions like the neutrino. This led him, in collaboration with [[Luis AlvarezGaumé]] to study violations of the conservation laws in gravity theories with [[Gravitational anomalyanomalies]], concluding that type I string theories were inconsistent. Green and Schwarz discovered a contribution to the anomaly that Witten and AlvarezGaumé had missed, which restricted the gauge group of the type I string theory to be SO(32). In coming to understand this calculation, Edward Witten became convinced that string theory was truly a consistent theory of gravity, and he became a highprofile advocate. Following Witten's lead, between 1984 and 1986, hundreds of physicists started to work in this field, and this is sometimes called the [[first superstring revolution]]. 

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During this period, [[David Gross]], [[Jeffrey A. HarveyJeffrey Harvey]], [[Emil Martinec]], and [[Ryan Rohm]] discovered [[heterotic strings]]. The gauge group of these closed strings was two copies of [[E8 (mathematics)E8]], and either copy could easily and naturally include the standard model. [[Philip Candelas]], [[Gary Horowitz]], [[Andrew Strominger]] and Edward Witten found that the CalabiYau manifolds are the compactifications that preserve a realistic amount of supersymmetry, while [[Lance Dixon]] and others worked out the physical properties of [[orbifolds]], distinctive geometrical singularities allowed in string theory. [[Cumrun Vafa]] generalized Tduality from circles to arbitrary manifolds, creating the mathematical field of [[mirror symmetry (string theory)mirror symmetry]]. [[Daniel Friedan]], [[Emil Martinec]] and [[Stephen Shenker]] further developed the covariant quantization of the superstring using conformal field theory techniques. [[David Gross]] and [[Vipul Periwal]] discovered that string perturbation theory was divergent. [[Stephen Shenker]] showed it diverged much faster than in field theory suggesting that new nonperturbative objects were missing. 

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In the 1990s, [[Joseph Polchinski]] discovered that the theory requires higherdimensional objects, called [[Dbrane]]s and identified these with the blackhole solutions of supergravity. These were understood to be the new objects suggested by the perturbative divergences, and they opened up a new field with rich mathematical structure. It quickly became clear that Dbranes and other pbranes, not just strings, formed the matter content of the string theories, and the physical interpretation of the strings and branes was revealed—they are a type of black hole. [[Leonard Susskind]] had incorporated the [[holographic principle]] of [[Gerardus 't Hooft]] into string theory, identifying the long highly excited string states with ordinary thermal black hole states. As suggested by 't Hooft, the fluctuations of the black hole horizon, the worldsheet or worldvolume theory, describes not only the degrees of freedom of the black hole, but all nearby objects too. 

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===Second superstring revolution=== 

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[[File:Edward Witten at Harvard.jpgthumb[[Edward Witten]]]] 

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In 1995, at the annual conference of string theorists at the University of Southern California (USC), [[Edward Witten]] gave a speech on string theory that in essence united the five string theories that existed at the time, and giving birth to a new 11dimensional theory called [[Mtheory]]. Mtheory was also foreshadowed in the work of [[Paul Townsend]] at approximately the same time. The flurry of activity that began at this time is sometimes called the [[second superstring revolution]]. 

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During this period, [[Tom Banks (Physicist)Tom Banks]], [[Willy Fischler]], [[Stephen Shenker]] and [[Leonard Susskind]] formulated matrix theory, a full holographic description of Mtheory using IIA D0 branes.<ref>{{cite journaldoi=10.1103/PhysRevD.55.5112arxiv=hepth/9610043v3title=M theory as a matrix model: A conjectureyear=1997last1=Banksfirst1=T.last2=Fischlerfirst2=W.last3=Shenkerfirst3=S. H.last4=Susskindfirst4=L.journal=Physical Review Dvolume=55issue=8pages=5112bibcode = 1997PhRvD..55.5112B }}</ref> This was the first definition of string theory that was fully nonperturbative and a concrete mathematical realization of the [[holographic principle]]. It is an example of a gaugegravity duality and is now understood to be a special case of the [[AdS/CFT]] correspondence. [[Andrew Strominger]] and [[Cumrun Vafa]] calculated the entropy of certain configurations of Dbranes and found agreement with the semiclassical answer for extreme charged black holes. [[Petr Hořava (theorist)Petr Hořava]] and Witten found the elevendimensional formulation of the heterotic string theories, showing that orbifolds solve the chirality problem. Witten noted that the effective description of the physics of Dbranes at low energies is by a supersymmetric gauge theory, and found geometrical interpretations of mathematical structures in gauge theory that he and [[Nathan Seiberg]] had earlier discovered in terms of the location of the branes. 

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In 1997, [[Juan Maldacena]] noted that the low energy excitations of a theory near a black hole consist of objects close to the horizon, which for extreme charged black holes looks like an [[anti de Sitter space]]. He noted that in this limit the gauge theory describes the string excitations near the branes. So he hypothesized that string theory on a nearhorizon extremecharged blackhole geometry, an antideSitter space times a sphere with flux, is equally well described by the lowenergy limiting [[gauge theory]], the ''N=4'' supersymmetric [[Yang–Mills theory]]. This hypothesis, which is called the [[AdS/CFT correspondence]], was further developed by [[Steven Gubser]], [[Igor Klebanov]] and [[Alexander Markovich PolyakovAlexander Polyakov]], and by [[Edward Witten]], and it is now wellaccepted. It is a concrete realization of the [[holographic principle]], which has farreaching implications for [[black hole]]s, [[Principle of localitylocality]] and [[information]] in physics, as well as the nature of the gravitational interaction. Through this relationship, string theory has been shown to be related to gauge theories like [[quantum chromodynamics]] and this has led to more quantitative understanding of the behavior of [[hadron]]s, bringing string theory back to its roots. 

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==Criticisms== 

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Some critics of string theory say that it is a failure as a [[theory of everything]].<ref name = "Wrong">Woit, Peter [http://www.math.columbia.edu/~woit/wordpress/?cat=2 Not Even Wrong]. Math.columbia.edu. Retrieved on 20120711.</ref><ref name = "Smolin">Smolin, Lee. [http://www.thetroublewithphysics.com The Trouble With Physics]. Thetroublewithphysics.com. Retrieved on 20120711.</ref><ref>[http://golem.ph.utexas.edu/category/2007/02/this_weeks_finds_in_mathematic_7.html The nCategory Cafe]. Golem.ph.utexas.edu (20070225). Retrieved on 20120711.</ref><ref>[http://math.ucr.edu/home/baez/week246.html John Baez weblog]. Math.ucr.edu (20070225). Retrieved on 20120711.</ref><ref>Woit, P. (Columbia University), ''String theory: An Evaluation'', February 2001, [[arXiv:physics/0102051]]</ref><ref>Woit, P. [http://www.math.columbia.edu/~woit/testable.pdf Is String Theory Testable?] INFN Rome March 2007</ref> Notable critics include [[Peter Woit]], [[Lee Smolin]], [[Philip Warren Anderson]],<ref>[http://www.nytimes.com/2005/01/04/science/04edgehed.html?pagewanted=3 God (or Not), Physics and, of Course, Love: Scientists Take a Leap], [[New York Times]], 4 January 2005: "String theory is the first science in hundreds of years to be pursued in preBaconian fashion, without any adequate experimental guidance"</ref> [[Sheldon Glashow]],<ref>"there ain't no experiment that could be done nor is there any observation that could be made that would say, `You guys are wrong.' The theory is safe, permanently safe" [http://pbs.org/wgbh/nova/elegant/viewglashow.html NOVA interview]</ref> [[Lawrence Krauss]],<ref>Krauss, Lawrence (8 November 2005) [http://www.nytimes.com/2005/11/08/science/08essay.html?_r=0 Science and Religion Share Fascination in Things Unseen]. ''[[New York Times]]'': "String theory [is] yet to have any real successes in explaining or predicting anything measurable".</ref> and [[Carlo Rovelli]].<ref>{{cite journaldoi=10.1142/S0218271803004304arxiv=hepth/0310077year=2003last1=Rovellifirst1=Carlojournal=International Journal of Modern Physics D [Gravitation; Astrophysics and Cosmology]volume=12issue=9pages=1509bibcode = 2003IJMPD..12.1509Rtitle=A Dialog on Quantum Gravity }}</ref> Some common criticisms include: 

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# Very high energies needed to test [[quantum gravity]]. 

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# Lack of uniqueness of predictions due to the large number of solutions. 

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# Lack of background independence. 

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===High energies=== 

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It is widely believed that any theory of [[quantum gravity]] would require extremely high energies to probe directly, higher by orders of magnitude than those that current experiments such as the [[Large Hadron Collider]]<ref>Kiritsis, Elias (2007) ''[http://press.princeton.edu/chapters/s8456.pdf String Theory in a Nutshell]'', Princeton University Press, ISBN1400839335.</ref> can attain. This is because strings themselves are expected to be only slightly larger than the [[Planck length]], which is twenty orders of magnitude smaller than the radius of a proton, and high energies are required to probe small length scales. Generally speaking, quantum gravity is difficult to test because gravity is much weaker than the other forces, and because quantum effects are controlled by Planck's constant [[Planck's constanth]], a very small quantity. As a result, the effects of quantum gravity are extremely weak. 

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===Number of solutions=== 

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String theory as it is currently understood has a huge number of solutions, called string vacua,<ref name = "KKLT">{{cite journaldoi=10.1103/PhysRevD.68.046005arxiv=hepth/0301240title=De Sitter vacua in string theoryyear=2003last1=Kachrufirst1=Shamitlast2=Kalloshfirst2=Renatalast3=Lindefirst3=Andreilast4=Trivedifirst4=Sandipjournal=Physical Review Dvolume=68issue=4bibcode = 2003PhRvD..68d6005K }}</ref> and these vacua might be sufficiently diverse to accommodate almost any phenomena we might observe at lower energies. 

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The vacuum structure of the theory, called the [[string theory landscape]] (or the anthropic portion of string theory vacua), is not well understood. String theory contains an infinite number of distinct metastable vacua, and perhaps 10<sup>520</sup> of these or more correspond to a universe roughly similar to ours—with four dimensions, a high planck scale, gauge groups, and chiral fermions. Each of these corresponds to a different possible universe, with a different collection of particles and forces.<ref name = "KKLT"/> What principle, if any, can be used to select among these vacua is an open issue. While there are no continuous parameters in the theory, there is a very large set of possible universes, which may be radically different from each other. It is also suggested that the landscape is surrounded by an even more vast [[swampland (physics)swampland]] of consistentlooking semiclassical effective field theories, which are actually inconsistent.{{Citation neededdate=April 2011}} 

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Some physicists believe this is a good thing, because it may allow a natural [[anthropic principleanthropic explanation]] of the observed values of [[physical constant]]s, in particular the small value of the [[cosmological constant]].<ref>ArkaniHamed, N.; Dimopoulos, S. and Kachru, S. ''Predictive Landscapes and New Physics at a TeV'', [[arXiv:hepth/0501082]], SLACPUB10928, HUTP05A0001, SUITP0444, January 2005</ref><ref>Susskind, L. ''The Anthropic Landscape of String Theory'', [[arXiv:hepth/0302219]], February 2003</ref> The argument is that most universes contain values for physical constants that do not lead to habitable universes (at least for humans), and so we happen to live in the "friendliest" universe. This principle is already employed to explain the existence of life on earth as the result of a lifefriendly orbit around the mediumsized sun among an infinite number of possible orbits (as well as a relatively stable location in the galaxy). 

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===Background independence=== 

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{{MainBackground independence}} 

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A separate and older criticism of string theory is that it is backgrounddependent—string theory describes perturbative expansions about fixed spacetime backgrounds which means that mathematical calculations in the theory rely on preselecting a background as a starting point. This is because, like many [[quantum field theoryquantum field theories]], much of string theory is still only formulated [[perturbation theory (quantum mechanics)perturbatively]], as a [[divergent series]] of approximations. Although the theory, defined as a perturbative expansion on a fixed background, is not background independent, it has some features that suggest nonperturbative approaches would be backgroundindependent—topology change is an established process in string theory, and the exchange of gravitons is equivalent to a change in the background. Since there are dynamic corrections to the background spacetime in the perturbative theory, one would expect spacetime to be dynamic in the nonperturbative theory as well since they would have to predict the same spacetime. 

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This criticism has been addressed to some extent by the [[AdS/CFT]] duality, which is believed to provide a full, nonperturbative definition of string theory in spacetimes with [[antide Sitter space]] asymptotics. Nevertheless, a [[nonperturbative]] definition of the theory in arbitrary spacetime backgrounds is still lacking. Some hope that [[Mtheory]], or a [[nonperturbative]] treatment of string theory (such as "background independent open [[string field theory]]") will have a backgroundindependent formulation. 

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== See also == 

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* [[Conformal field theory]] 

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* [[Glossary of string theory]] 

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* [[List of string theory topics]] 

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* [[Loop quantum gravity]] 

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* [[Supergravity]] 

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* [[Supersymmetry]] 

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==References== 

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{{Reflist2}} 

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==Further reading== 

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===Popular books=== 

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====General==== 

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* {{Cite book first = Paul  last = Davies  authorlink = Paul Davies  coauthors = Julian R. Brown (Eds.)  year = 1992  title = Superstrings: A Theory of Everything?  publisher = Cambridge University Press  location = Cambridge  isbn = 052143775X }} 

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* {{Cite book first = Brian  last = Greene  authorlink = Brian Greene  year = 2003  title = [[The Elegant UniverseThe Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory]]  publisher = W.W. Norton & Company  location = New York  isbn = 0393058581 }} 

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* {{Cite book first = Brian  last = Greene  authorlink = Brian Greene  year = 2004  title = [[The Fabric of the Cosmos: Space, Time, and the Texture of Reality]]  publisher = Alfred A. Knopf  location = New York  isbn = 0375412883 }} 

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* {{Cite book first = Michio  last = Kaku  authorlink = Michio Kaku  year = 1994  title = Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension  publisher = Oxford University Press  location = Oxford  isbn = 0195085140 }} 

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* {{Cite book first = George  last = Musser  authorlink = George Musser  year = 2008  title = The Complete Idiot's Guide to String Theory  publisher = Alpha  location = Indianapolis  isbn = 9781592577026 }} 

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* {{Cite book first = Lisa  last = Randall  authorlink = Lisa Randall  year = 2005  title = [[Warped Passages]]: Unraveling the Mysteries of the Universe's Hidden Dimensions  publisher = Ecco Press  location = New York  isbn = 0060531088 }} 

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* {{Cite book first = Leonard  last = Susskind  authorlink = Leonard Susskind  year = 2006  title = [[Leonard Susskind#The Cosmic LandscapeThe Cosmic Landscape]]: String Theory and the Illusion of Intelligent Design  publisher = Hachette Book Group/Back Bay Books  location = New York  isbn = 0316013331 }} 

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* {{Cite book first1 = ShingTung  last1 = Yau  authorlink = ShingTung 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 = 9780465020232 }} 

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====Critical==== 

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* {{Cite book first = Roger  last = Penrose  authorlink = Roger Penrose  year = 2005  title = [[The Road to Reality]]: A Complete Guide to the Laws of the Universe  publisher = Knopf  isbn = 0679454438 }} 

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* {{Cite book first = Lee  last = Smolin  authorlink = Lee 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 = 0618551050 }} 

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* {{Cite book first = Peter  last = Woit  authorlink = Peter Woit  year = 2006  title = Not Even Wrong: The Failure of String Theory And the Search for Unity in Physical Law  publisher = New York: Basic Books  location = London: Jonathan Cape &  isbn = 9780465092758 <! both are correct >}} 

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===Textbooks=== 

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====For physicists==== 

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* Becker, Katrin, Becker, Melanie, and [[John H. SchwarzSchwarz, John]] (2007) ''String Theory and MTheory: A Modern Introduction ''. Cambridge University Press. ISBN 0521860695 

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* Dine, Michael (2007) ''Supersymmetry and String Theory: Beyond the Standard Model''. Cambridge University Press. ISBN 0521858410. 

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* Kiritsis, Elias (2007) ''String Theory in a Nutshell''. Princeton University Press. ISBN 9780691122304. 

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* [[Michael Green (physicist)Michael Green]], [[John H. Schwarz]] and [[Edward Witten]] (1987) ''Superstring theory''. Cambridge University Press. 

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** ''Vol. 1: Introduction''. ISBN 0521357527. 

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** ''Vol. 2: Loop amplitudes, anomalies and phenomenology''. ISBN 0521357535. 

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* {{Cite book first = Clifford  last = Johnson  year = 2003  title = Dbranes  publisher = Cambridge University Press  location = Cambridge  isbn = 0521809126 }} 

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* [[Joseph PolchinskiPolchinski, Joseph]] (1998) ''String theory''. Cambridge University Press. 

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** ''Vol. 1: An Introduction to the Bosonic String''. ISBN 0521633036. 

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** ''Vol. 2: Superstring Theory and Beyond''. ISBN 0521633044. 

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* Szabo, Richard J. (2007) ''An Introduction to String Theory and Dbrane Dynamics''. Imperial College Press. ISBN 9781860944277. 

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* [[Barton ZwiebachZwiebach, Barton]] (2004) ''A First Course in String Theory''. Cambridge University Press. ISBN 0521831431. 

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====For mathematicians==== 

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* {{cite book editor1first=Paul editor1last=Aspinwall editor2first=Tom editor2last=Bridgeland editor3first=Alastair editor3last=Craw editor4first=Michael editor4last=Douglas editor5first=Mark editor5last=Gross editor6first=Anton editor6last=Kapustin editor7first=Gregory editor7last=Moore editor8first=Graeme editor8last=Segal editor9first=Balázs editor9last=Szendröi editor10first=P.M.H. editor10last=Wilson title=Dirichlet Branes and Mirror Symmetry year=2009 publisher=American Mathematical Society}} 

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* {{cite book editor1first=Pierre editor1last=Deligne editor2first=Pavel editor2last=Etingof editor3first=Daniel editor3last=Freed editor4first=Lisa editor4last=Jeffery editor5first=David editor5last=Kazhdan editor6first=John editor6last=Morgan editor7first=David editor7last=Morrison editor8first=Edward editor8last=Witten title=Quantum Fields and Strings: A Course for Mathematicians year=1999 publisher=American Mathematical Society isbn=0821820125}} 

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* {{cite book editor1first=Kentaro editor1last=Hori editor2first=Sheldon editor2last=Katz editor3first=Albrecht editor3last=Klemm editor4first=Rahul editor4last=Pandharipande editor5first=Richard editor5last=Thomas editor6first=Cumrun editor6last=Vafa editor7first=Ravi editor7last=Vakil editor8first=Eric editor8last= Zaslowtitle=Mirror Symmetry year=2003 publisher=American Mathematical Societyurl=http://math.stanford.edu/~vakil/files/mirrorfinal.pdfisbn=0821829556}} 

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===Online material=== 

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* [[Igor KlebanovKlebanov, Igor]] and [[Juan MaldacenaMaldacena, Juan]] (January 2009). "[http://ptonline.aip.org/journals/doc/PHTOADft/vol_62/iss_1/28_1.shtml Solving Quantum Field Theories via Curved Spacetimes]". ''[[Physics Today]]''. 

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* {{Cite arXiv author=[[John H. SchwarzSchwarz, John H.]]  title=Introduction to Superstring Theory  eprint=hepex/0008017 class=hepex year=2000}} 

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* {{cite journal author=Witten, Edward  title=The Universe on a String  journal=[[Astronomy Magazine]]  month=June  year=2002  url=http://www.sns.ias.edu/~witten/papers/string.pdf format=PDF accessdate=December 19, 2005  authorlink= Edward Witten}} 

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* {{cite web author=Witten, Edward  title=Duality, Spacetime and Quantum Mechanics  publisher=Kavli Institute for Theoretical Physics  year=1998  url=http://online.itp.ucsb.edu/online/plecture/witten/  accessdate=December 16, 2005  authorlink= Edward Witten}} 

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* {{cite journal author=Woit, Peter  title=Is string theory even wrong?  journal=[[American Scientist]]  year=2002  url=http://www.americanscientist.org/issues/pub/isstringtheoryevenwrong  accessdate=December 16, 2005  authorlink= Peter Woit}} 

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==External links== 

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{{Wiktionary}} 

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

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* [http://www.mathpages.com/home/kmath632/kmath632.htm Dialogue on the Foundations of String Theory] at MathPages 

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* [http://www.sukidog.com/jpierre/strings/ Superstrings! String Theory Home Page]—Online tutorial 

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* [http://zidbits.com/2011/03/alaymansexplanationforstringtheory/ A Layman’s Guide to String Theory]—An explanation for the layperson 

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

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* [http://superstringtheory.com/ The Official String Theory Web Site] 

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* [http://www.pbs.org/wgbh/nova/elegant/ ''The Elegant Universe'']—A threehour miniseries with [[Brian Greene]] by ''NOVA'' (original PBS Broadcast Dates: October 28, 8–10 p.m. and November 4, 8–9 p.m., 2003). Various images, texts, videos and animations explaining string theory. 

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* [http://www.phys.ens.fr/~troost/beyondstringtheory/ Beyond String Theory]—A project by a string physicist explaining aspects of string theory to a broad audience 

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{{DEFAULTSORT:String Theory}} 

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[[Category:String theory]] 

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[[Category:Concepts in physics]] 

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[[Category:Dimension]] 

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[[Category:Multidimensional geometry]] 

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[[Category:Particle physics]] 

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[[Category:Physical cosmology]] 

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[[Category:Physics beyond the Standard Model]] 

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[[Category:Theoretical physics]] 

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{{Link GAru}} 

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{{Link FAla}} 
