View source for User:Mpatel/sandbox/String theory

{{update}}
{{Otheruses4|the branch of theoretical physics}}
{{String theory|cTopic=Theory}} 

'''String theory''' is a developing branch of [[theoretical physics]] that combines [[quantum mechanics]] and [[general relativity]] into a [[quantum gravity|quantum theory of gravity]].<ref>Sunil Mukhi(1999)"[http://theory.tifr.res.in/~mukhi/Physics/string2.html The Theory of Strings: A Detailed Introduction]"</ref>  The [[String (physics)|string]]s of string theory are one-dimensional oscillating lines, but they are no longer considered fundamental to the theory, which can be formulated in terms of points or surfaces, too. 

Since its birth as the [[dual resonance model]] which described the strongly interacting [[hadron]]s as strings, the term ''string theory'' has changed to include any of a group of related [[superstring theory|superstring theories]] which unite them. One shared property of all these theories is the [[holographic principle]]. String theory itself comes in many different formulations, each one with a different mathematical structure, and each best describing different physical circumstances. But the principles shared by these approaches, their mutual logical consistency, and the fact that some of them easily include the [[standard model of particle physics]], has led many physicists to believe that the theory is the correct fundamental description of nature. In particular, string theory is the first candidate for the [[theory of everything]] (TOE), a way to describe the known [[fundamental interaction|fundamental force]]s ([[gravity|gravitational]], [[electromagnetism|electromagnetic]], [[weak interaction|weak]] and [[strong interaction|strong]] interactions) and matter ([[quark]]s and [[lepton]]s) in a mathematically complete system. 

Many detractors criticize string theory as it has not provided quantitative experimental predictions. Like any other quantum theory of gravity, it is widely believed that testing the theory directly would require prohibitively expensive feats of engineering. Whether there are stringent indirect tests of the theory is unknown.

String theory is of interest to many [[physicist]]s because it requires new mathematical and physical ideas to mesh together its very different mathematical formulations. One of the most inclusive of these is the 11-dimensional [[M-theory]], which requires spacetime to have eleven dimensions,<ref>M. J. Duff, James T. Liu and R. Minasian [http://arxiv.org/abs/hep-th/9506126v2 Eleven Dimensional Origin of String/String Duality: A One Loop Test] Center for Theoretical Physics, Department of Physics, Texas A&M University</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 M-theory 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 not described by a real number, but by a completely different type of mathematical quantity. So the notion of spacetime dimension is not fixed in string theory: it is best thought of as different in different circumstances.<ref>Polchinski, Joseph (1998). ''String Theory'', Cambridge University Press.</ref>

String theories include objects more general than strings, called [[p-brane|brane]]s.  The word ''brane'', derived from "membrane", refers to a variety of interrelated objects, such as [[D-branes]], black p-branes and [[Neveu-Schwarz]] 5-branes.  These are extended objects that are charged sources for [[differential form]] generalizations of the [[vector potential]] electromagnetic field.  These objects are related to one-another by a variety of dualities.  Black hole-like black p-branes are identified with [[D-branes]], which are endpoints for strings, and this identification is called [[String theory#Gauge-gravity duality|Gauge-gravity duality]]. Research on this equivalence has led to new insights on [[quantum chromodynamics]], the fundamental theory of the [[strong interaction|strong nuclear force]].<ref name="autogenerated2">H. Nastase, ''The RHIC fireball as a dual black hole'', BROWN-HET-1439, [[arXiv:hep-th/0501068]], January 2005,</ref><ref name="autogenerated1">H. Nastase, ''More on the RHIC fireball and dual black holes'', BROWN-HET-1466, [[arXiv:hep-th/0603176]], March 2006,</ref><ref name="autogenerated3">H. Liu, K. Rajagopal, U. A. Wiedemann, ''An AdS/CFT Calculation of Screening in a Hot Wind'', MIT-CTP-3757, [[arXiv:hep-ph/0607062]] July 2006,</ref><ref name="autogenerated4">H. Liu, K. Rajagopal, U. A. Wiedemann, ''Calculating the Jet Quenching Parameter from AdS/CFT'', Phys.Rev.Lett.97:182301,2006 [[arXiv:hep-ph/0605178]]</ref>

==History==
{{Main|History of string theory}}

<!-- NEW HISTORY 
Hadrons, formulae describing strings, S-matrix, dual resonance model, regge trajectories 
Supersymmetry and superstrings
Superstring revolutions, duality, D-branes, M-theory, holographic principle, F-theory, string cosmology -->


<!-- Keep this -->
String theory was originally developed during the late 1960s and early 1970s as a never completely successful theory of [[hadron]]s, [[subatomic particle]]s (such as the [[proton]] and [[neutron]]) which feel the [[strong interaction]]. 

[[Geoffrey Chew]] and [[Steven Frautschi]] discovered that [[meson]]s make families called [[Regge trajectories]] with masses related to [[spin]]s 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 which did not presume that they were composed of any fundamental particles, but would construct their interactions from [[bootstrap model|self-consistency conditions]] on the [[S-matrix]]. The [[S-matrix theory|S-matrix approach]] was started by [[Werner Heisenberg]] in the 1940s as a way of constructing a theory which 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, hesienberg's approach was ideally suited for a theory of quantum gravity.  

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 [[fifth 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 a [[Kaluza-Klein theory|physical interpretation]] of the unobservable extra dimension--- it is wrapped into a small circle. Einstein introduced a non-symmetric geometric 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.

Working with experimental data, R. Dolen, D. Horn and C. Schmidt developed [[sum rule]]s for hadron exchange. When a particle and antiparticle scatter, virtual particles can be exchanged in two qualitatively different ways. In the s-channel, the two particles annihilate to make temporary intermediate states which fall apart into the final state particles. In the t-channel, 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 t-channel contribution was dual to the s-channel one, meaning both described the whole amplitude and included the other.

The result was widely advertised by [[Murray Gell-Mann]], leading [[Gabriele Veneziano]] to constructed  a scattering amplitude which had the property of Dolen-Horn-Schmidt duality, later renamed world-sheet 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 near-beam scattering data as well as other Regge type fits, and had a suggestive integral representation which could be used for generalization.

Over the next years, hundreds of physicists worked to complete the bootstrap program for this model, with many surprises. Veneziano himself discovered that for the scattering amplitude to describe the scattering of a particle which appears in the theory, an obvious self-consistency condition, the lightest particle must be a [[tachyon]]. [[Miguel Angel Virasoro|Miguel Virasoro]] and Joel Shapiro found a different amplitude now understood to be that of closed strings, while [[Ziro Koba]] and [[Holger Bech Nielsen|Holger Nielsen]] generalized Veneziano's integral representation to multiparticle scattering. Veneziano and [[Sergio Fubini]] introduced an operator formalism for computing the scattering amplitudes which was a forerunner of world-sheet conformal theory, while Virasoro understood how to remove the poles with wrong-sign 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]] and [[Richard Brower]] went on to prove that there are no wrong-sign propagating states in dimensions less than or equal to 26.

In 1969 [[Yoichiro Nambu|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]], [[Jeffrey Goldstone]], [[Claudio Rebbi]] and [[Charles Thorn]], giving a space-time picture to the vertex operators introduced by Veneziano and Fubini and a geometrical interpretation to the [[Virasoro algebra|Virasoro conditions]].

In 1970, [[Pierre Ramond]] added fermions to the model, which led him to formulate a two-dimensional supersymmetry to cancel the wrong-sign states. [[John Henry Schwarz|John 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 two-dimensional field theoretic path-integral 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.

In 1974, [[Tamiaki Yoneya]] discovered that all string theories include a massless spin-two particle which 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]].

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 the work of a handful of devotees. [[Ferdinando Gliozzi]], Joel Scherk, and [[David Olive]] realized in 1976 that the original Ramond and Neveu Schwarz-strings were separately inconsistent and needed to be combined. The resulting theory did not have a tachyon, and was proven to have space-time supersymmetry by John Schwarz and [[Michael Green (physicist)|Michael Green]] in 1981. The same year, [[Alexander 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 two-dimensional field theory. Schwarz and Green discovered T-duality, and constructed two different superstring theories--- IIA and IIB related by T-duality, 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.

In the early 1980s, [[Edward Witten]] discovered that most quantum gravity theories could not accommodate [[chiral]] fermions like the neutrino. This led him, in collaboration with [[Luis Alvarez-Gaumé]] to study violations of the [[conservation law]]s in gravity theories with [[Gravitational anomaly|anomalies]], concluding that type I string theories were inconsistent. Green and Schwarz discovered a contribution to the anomaly that Witten and Alvarez-Gaumé 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 high-profile advocate. Following Witten's lead, between 1984 and 1986 hundreds of physicists worked in this field, thus commencing the [[first superstring revolution]]. 

During this period, [[David Gross]], [[Jeffrey Harvey]], [[Emil Martinec]], and [[Ryan Rohm]] discovered [[heterotic strings]]. The gauge group of these closed strings was two copies of E8, and either copy could easily and naturally include the standard model. [[Philip Candelas]], [[Gary Horowitz]], [[Andrew Strominger]] and Witten found that the Calabi-Yau manifolds are the compactifications which 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 T-duality from circles to arbitrary manifolds, creating the mathematical field of [[mirror symmetry]]. [[David Gross]] and [[Vipul Periwal]] discovered that string perturbation theory was divergent in a way that suggested that new non-perturbative objects were missing.

<!-- Keep -->
During this period, it became clear that there are five consistent string theories called type I, type IIA, type IIB, E8 X E8 heterotic (HE), and SO(32) heterotic (HO). 

In the 1990s, [[Joseph Polchinski]] discovered that the theory requires higher-dimensional objects, called [[D-brane]]s and identified these with the black-hole 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 D-branes and other p-branes, 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|Susskind]] 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, fluctuations of the black hole horizon, the world-sheet or world-volume theory, describes not only the [[degrees of freedom]] of the black hole, but all nearby objects too.

<!-- Keep -->
The [[second superstring revolution]] began in 1995 when [[Edward Witten|Witten]] gave a speech on string theory that essentially united the five existing string theories. The result, a new 11-dimensional theory called [[M-theory]], was also foreshadowed in the work of [[Paul Townsend]] at approximately the same time. 

During this period,  [[Tom Banks (Physicist)|Tom Banks]], [[Willy Fischler]] [[Stephen Shenker]] and [[Leonard Susskind]] formulated a full holographic description of M-theory on IIA D0 branes, the first definition of string theory that was fully non-perturbative and a concrete mathematical realization of the [[holographic principle]]. [[Andrew Strominger]] and [[Cumrun Vafa]] calculated the entropy of certain configurations of D-branes and found agreement with the semi-classical answer for extreme charged black holes. [[Petr Horava]] and Witten found the eleven-dimensional formulation of the heterotic string theories, showing that [[orbifold]]s solve the chirality problem. Witten noted that the effective description of the physics of D-branes 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.

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 near-horizon extreme-charged black-hole geometry, an anti-deSitter space times a sphere with flux, is equally well described by the low-energy limiting [[gauge theory]], the ''N=4'' supersymmetric [[Yang-Mills theory]]. This well-accepted hypothesis, complemented by converging work due to [[Steven Gubser]], [[Igor Klebanov]] and [[Alexander Polyakov|Polyakov]], is called the [[AdS/CFT correspondence]]. It is a concrete realization of the [[holographic principle]], which has far-reaching implications for [[black hole]]s, [[Principle of locality|locality]] 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.

==Overview==

{{See also|Quantum gravity}}

String theory posits that the [[electron]]s and [[quark]]s within an [[atom]] are modelled not as 0-dimensional objects ([[Point (geometry)|point]]s), but 1-dimensional strings. These strings can move and vibrate, giving the observed particles their [[Flavor (particle physics)|flavor]], [[Charge (physics)|charge]], [[mass]] and [[spin (physics)|spin]]. The strings make closed loops unless they encounter surfaces, called [[D-brane]]s, where they can open up into 1-dimensional lines. The endpoints of the string cannot break off the D-brane, but they can slide around on it.
[[Image:String theory.svg|right|thumb|250px|Levels 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]]

String theory is a theory of gravity, an extension of [[General Relativity]], and the classical interpretation of strings and branes is that they are [[quantum mechanics|quantum mechanical]] vibrating, extended charged [[black hole]]s. The overarching physical insight behind string theory is the [[holographic principle]], which states that the description of the oscillations of the surface of a [[black hole]] must also describe the spacetime around it. Holography demands that a low-dimensional theory describing the fluctuations of a horizon will end up describing everything that can fall through, which can be anything at all. So a theory of a black hole horizon is a theory of everything.

Finding even one consistent holographic description, ''a priori'', seems like a long-shot, because it would be a disembodied nonlocal description of quantum gravity. In string theory, not only is there one such description, there are several different ones, each describing fluctuations of horizons with different charges and dimensions, and all of them logically fit together. So the same physical objects and interactions can be described by the fluctuations of [[dual resonance model|one-dimensional black hole horizons]], or by [[AdS/CFT correspondence|three-dimensional horizons]], or by [[matrix string theory|zero-dimensional horizons]]. The fact that these different descriptions describe the same physics is evidence that string theory is consistent.

An ordinary astronomical black hole does not have a convenient holographic description, because it has a [[Hawking radiation|Hawking temperature]]. String theories are formulated on cold black holes, which are those which have as much charge as possible. The first holographic theory described the scattering of one-dimensional strings, tiny loops of vibrating horizon charged with a [[differential form|two-form]] vector potential which makes a charged black hole a one-dimensional line. Fluctuations of this line horizon describe all matter, so every [[elementary particle]] can be described by a mode of oscillation of a very small segment or loop of [[string (physics)|string]]. The string-length is approximately the [[Planck length]], but can be significantly bigger when the strings are weakly interacting.

All string theories predict the existence of [[degrees of freedom (physics and chemistry)|degrees of freedom]] which are usually described as [[String theory#Extra dimensions|extra dimensions]]. Without fermions, bosonic strings can vibrate in a flat but unstable 26-dimensional space time. In a [[superstring theory]] with fermions, the weak-coupling (no-interaction) limit describes a flat stable 10-dimensional space time. Interacting superstring theories are best thought of as configurations of an 11 dimensional supergravity theory called [[M-theory]] where one or more of the dimensions are curled up so that the line-extended charged black holes become long and light.

Long, light strings can vibrate at different [[resonance|resonant]] frequencies, each such [[frequency]] describing a different elementary particle.<ref>To compare, the size of an atom is roughly 10<sup>-10</sup> m and the size of a proton is 10<sup>-15</sup> m. To imagine the [[Planck length]]: you can stretch along the [[diameter]] of an [[atom]] the same number of strings as the number of atoms you can line up to [[Proxima Centauri]] (the nearest [[star]] to [[Earth]] after the [[Sun]]). The [[Tension (mechanics)|tension]] of a string (8.9×10<sup>42</sup> [[newton]]s) is about 10<sup>41</sup> times the tension of an average [[piano]] string (735 newtons).</ref> So in string limits, any [[elementary particle]] should be thought of as a tiny vibrating line, rather than as a point. The string can vibrate in different modes just as a guitar string can produce different notes, and every mode appears as a different particle: [[electron]], [[photon]], [[gluon]], etc.

The only way in which strings can interact is by splitting and combining in a smooth way. It is impossible to introduce arbitrary extra matter, like point particles which interact with strings by collisions, because the particles can fall into the black hole, so holography demands that it must show up as a mode of oscillation. The only way to introduce new matter is to find gravitational backgrounds where strings can scatter consistently, or to add [[boundary conditions]], endpoints for the strings. Some of the backgrounds are called [[NS-brane]]s, which are extreme-charged black hole sheets of different dimensions. Other charged black-sheet backgrounds are the [[D-branes]], which have an alternate description as planes where strings can end and slide. When the strings are long and light, the branes are classical and heavy. In other limits where the strings become heavy, some of the branes can become light.

Since string theory is widely believed to be a consistent theory of [[quantum gravity]], many hope that it correctly describes our universe, making it a [[theory of everything]]. There are known configurations which describe all the observed fundamental forces and matter but with a zero cosmological constant and some new fields. There are other configurations with different values of the cosmological constant, which are [[metastable]] but long-lived. This leads many to believe that there is at least one metastable solution which is quantitatively identical with the [[standard model]], with a small cosmological constant, which contains dark matter and a plausible mechanism for [[cosmic inflation|inflation]]. It is not yet known whether string theory has such a solution, nor how much freedom the theory allows to choose the details. 

The full theory does not yet have a satisfactory definition in all circumstances, since the scattering of strings is most straightforwardly defined by a [[Perturbation theory (quantum mechanics)|perturbation theory]]. The complete [[quantum mechanics]] of high dimensional branes is not easily defined, and the behavior of string theory in cosmological settings (time-dependent backgrounds) is not fully worked out. It is also not clear if there is any principle by which string theory selects its [[vacuum state]], the spacetime configuration which determines the properties of our Universe (see [[string theory landscape]]).

== Formulation ==
{{Main|Mathematical formulation of string theory}}

==Properties==
String theory can be formulated in terms of an [[action (physics)|action]] principle, either the [[Nambu-Goto action]] or the [[Polyakov action]], which describes how strings move through space and time. In the absence of external interactions, string dynamics are governed by tension and kinetic energy, which combine to produce oscillations. The [[quantum mechanics]] of strings implies these oscillations take on discrete vibrational modes, the [[energy spectrum|spectrum]] of the theory.

On distance scales larger than the string radius, each oscillation mode behaves as a different species of particle, with its mass, spin and charge determined by the string's dynamics.  Splitting and recombinations of string 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 but distinct musical notes. In the analogy, different notes correspond to different particles. The only difference is the guitar is only 2-dimensional, you can strum it up, and down. In actuality the guitar strings would be every dimension, and the strings could vibrate in any direction. Meaning that the particles could move through not only our dimension, but other dimensions as well.

String theory includes both ''open'' strings, which have two distinct endpoints, and ''closed'' strings making a complete loop. The two [[String (physics)#Types of strings|types of string]] behave in slightly different ways, yielding two different spectra. For example, in most string theories, one of the closed string modes is the [[graviton]], and one of the open string modes is the [[photon]]. Because the two ends of an open string can always meet and connect, forming a closed string, there are no string theories without closed strings.

The earliest string model, the [[bosonic string theory|bosonic string]], incorporated only [[boson]]s.  This model describes, in low enough energies, a quantum [[gravity]] theory, which also includes (if open strings are incorporated as well) [[gauge field]]s such as the photon (or, more generally, any [[gauge theory]]). However, this model has problems. Most importantly, the theory has a fundamental instability, believed to result in the decay (at least partially) of spacetime itself. Additionally, 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 [[fermion]]s in its spectrum led to the invention of [[supersymmetry]], a mathematical relation between bosons and fermions. String theories which include fermionic vibrations are now known as [[superstring theory|superstring theories]]; several different kinds have been described, but all are now thought to be different limits of [[M-theory]].

Some qualitative properties of quantum strings can be understood in a fairly simple fashion. For example, quantum strings have tension, much like regular strings made of [[twine]]; this tension is considered a fundamental parameter of the theory. The tension of a quantum string is closely related to its size. Consider a closed loop of string, left to move through space without external forces. Its tension will tend to contract it into a smaller and smaller loop. Classical intuition suggests that it might shrink to a single point, but this would violate [[Werner Heisenberg|Heisenberg]]'s [[uncertainty principle]]. The characteristic size of the string loop will be a balance between the tension force, acting to make it small, and the uncertainty effect, which keeps it "stretched". Consequently, the minimum size of a string is related to the string tension.

===Worldsheet===
{{details|Relationship between string theory and quantum field theory}}
A point-like particle's motion may be described by drawing a graph of its position (in one or two dimensions of space) against time. The resulting picture depicts the [[worldline]] of the particle (its 'history') in [[spacetime]]. By analogy, a similar graph depicting the progress of a ''string'' as time passes by can be obtained; the string (a one-dimensional object — a small line — by itself) will trace out a surface (a two-dimensional [[manifold]]), known as the [[worldsheet]]. The different string modes (representing different particles, such as [[photon]] or [[graviton]]) are surface waves on this manifold.

A [[String (physics)#Types of strings|closed string]] looks like a small loop, so its worldsheet will look like a pipe or, more generally, a [[Riemann surface]] (a two-dimensional [[orientability|oriented manifold]]) with no boundaries (i.e. no edge).
An open string looks like a short line, so its worldsheet will look like a strip or, more generally, a [[Riemann surface]] with a boundary.

[[Image:World lines and world sheet.svg|right|thumb|300px|Interaction in the subatomic world: [[world line]]s of point-like [[Subatomic particle|particle]]s in the 
[[Standard Model]] or a [[world sheet]] swept up by closed [[string (physics)|strings]] in string theory]]

Strings can split and connect. This is reflected by the form of their worldsheet (more accurately, by its [[topology]]). For example, if a closed string splits, its worldsheet will look like a single pipe splitting (or connected) to two pipes (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 ingoing string, and the other — the outgoing one). An open string doing the same thing will have its worldsheet looking like a ring connected to two strips.

Note that the process of a string splitting (or strings connecting) is a global process of the worldsheet, not a local one: locally, the worldsheet looks the same everywhere and it is not possible to determine a single point on the worldsheet where the splitting occurs. Therefore these processes are an integral part of the theory, and are described by the same dynamics that controls the string modes.

In some string theories (namely, closed strings in [[Type I string|Type I]] and some versions of the [[bosonic string theory|bosonic string]]), strings can split and reconnect in an opposite orientation (as in a [[Möbius strip]] or a [[Klein bottle]]). These theories are called ''unoriented''. Formally, the worldsheet in these theories is a [[orientability|non-orientable surface]].

===Dualities===
{{Main|String duality|S-duality|T-duality|U-duality}}

Before the 1990s, string theorists believed there were five distinct superstring theories: open [[type I string|type I]], closed [[type I string|type I]], closed [[type IIA string|type IIA]], closed [[type IIB string|type IIB]], and the two flavors of [[heterotic string]] theory ([[special orthogonal group|SO(32)]] and [[E8 (mathematics)|''E''<sub>8</sub>×''E''<sub>8</sub>]])<ref>S. James Gates, Jr., Ph.D., [http://www.teach12.com/ttcx/coursedesclong2.aspx?cid=1284 Superstring Theory: The DNA of Reality] "Lecture 23 - Can I Have that Extra Dimension in the Window?", 0:04:54, 0:21:00.</ref>. 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 connected to one another as if they are each a special case of some more fundamental theory (thought to be [[M-theory]]). These theories are related by transformations that are called dualities. If two theories are related by a duality transformation, it means that the first theory can be transformed in some way so that it ends up looking just like the second theory. The two theories are then said to be dual to one another under that kind of transformation. Put differently, the two theories are mathematically different descriptions of the same phenomena.

These dualities link quantities that were also thought to be separate. 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 [[field theory]] and quantum [[particle 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. T-duality relates the large and small distance scales between string theories, whereas S-duality relates strong and weak coupling strengths between string theories. U-duality links T-duality and S-duality.

{|class="wikitable" mm_noconvert="TRUE"
|- bgcolor="#FFFFFF"
! colspan="3" class="dark" | String theories
|-
! class="dark" | Type
! class="dark" | Spacetime dimensions<br>
! class="dark" | Details
|-
! class="dark" | Bosonic
| align="CENTER" class="dark" | 26
| class="dark" | Only [[boson]]s, no [[fermion]]s, meaning only forces, no matter, with both open and closed strings; major flaw: a [[Particle physics|particle]] with imaginary mass, called the [[tachyon]], representing an instability in the theory.
|-
! class="dark" | I
| align="CENTER" class="dark" | 10
| class="dark" | [[Supersymmetry]] between forces and matter, with both open and closed strings; no [[tachyon]]; group symmetry is [[special orthogonal group|SO(32)]]
|-
! class="dark" | IIA
| align="CENTER" class="dark" | 10
| class="dark" | [[Supersymmetry]] between forces and matter, with closed strings and open strings bound to [[D-brane]]s; no [[tachyon]]; massless [[fermion]]s are non-[[Chirality (physics)|chiral]]
|-
! class="dark" | IIB
| align="CENTER" class="dark" | 10
| class="dark" | [[Supersymmetry]] between forces and matter, with closed strings and open strings bound to [[D-brane]]s; no [[tachyon]]; massless [[fermion]]s are [[Chirality (physics)|chiral]]
|-
! class="dark" | HO 
| align="CENTER" class="dark" | 10
| class="dark" | [[Supersymmetry]] between forces and matter, with closed strings only; no [[tachyon]]; [[heterotic]], meaning right moving and left moving strings differ; group symmetry is [[special orthogonal group|SO(32)]]
|-
! class="dark" | HE 
| align="CENTER" class="dark" | 10
| class="dark" | [[Supersymmetry]] between forces and matter, with closed strings only; no [[tachyon]]; [[heterotic]], meaning right moving and left moving strings differ; group symmetry is [[E8 (mathematics)|''E''<sub>8</sub>×''E''<sub>8</sub>]]
|}

Note that in the type IIA and type IIB string theories closed strings are allowed to move everywhere throughout the ten-dimensional spacetime (called the ''bulk''), while open strings have their ends attached to [[D-brane]]s, which are membranes of lower dimensionality (their dimension is odd — 1, 3, 5, 7 or 9 — in type IIA and even — 0, 2, 4, 6 or 8 — in type IIB, including the time direction).

===Extra dimensions===
====Number of dimensions====
An intriguing feature of string theory is that it involves the prediction of extra dimensions. The number of dimensions is not fixed by any consistency criterion, but [[flat spacetime]] solutions do exist in the so-called "critical dimension".  Cosmological solutions exist in a wider variety of dimensionalities, and these different dimensions&mdash;more precisely different values of the "effective central charge", a count of degrees of freedom which reduces to dimensionality in weakly curved regimes&mdash;are related by dynamical transitions.<ref>Simeon Hellerman and Ian Swanson(2006): "[http://arxiv.org/abs/hep-th/0612051v3 Dimension-changing exact solutions of string theory]".; Ofer Aharony and Eva Silverstein(2006):"[Supercritical stability, transitions and (pseudo)tachyons http://arxiv.org/abs/hep-th/0612031v2]".</ref> 

Nothing in [[James Clerk Maxwell|Maxwell]]'s theory of [[electromagnetism]] or [[Albert Einstein|Einstein]]'s [[theory of relativity]] makes this kind of prediction; these theories require physicists to insert the number of dimensions "by hand", and this number is fixed and independent of potential energy. String theory allows one to relate the number of dimensions to scalar potential energy. Technically, 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.

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 mass|massless]]. The mass of the photon which is predicted by string theory depends on the energy of the string mode which represents the photon. This energy includes a contribution from the [[Casimir effect]], namely from quantum fluctuations 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&mdash;and the theory consistent&mdash;only for a particular number of dimensions.<ref>The calculation of the number of dimensions can be circumvented by adding a [[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 which don't appear in nature. This is known as the ''[[linear dilaton]]'' or [[non-critical string]].</ref>

When the calculation is done, the critical dimensionality is not four as one may expect (three axes of space and one of time).
The subset of X is equal to the relation of photon fluxuations in a linear dimension. Flat space string theories are 26-dimensional in the bosonic case, while superstring and M-theories turn out to involve 10 or 11 dimensions for flat solutions. In bosonic string theories, the 26 dimensions come from the Polyakov equation.<ref>[ftp://ftp2.biblioteca.cbpf.br/pub/apub/1999/nf/nf_zip/nf04299.pdf "Quantum Geometry of Bosonic Strings &ndash; Revisited"]</ref> Starting from any dimension greater than four, it is necessary to consider how these are reduced to four dimensional [[spacetime]].

[[Image:Calabi-Yau.png|right|thumb|200px|[[Calabi-Yau manifold]] ([[3D projection]])]]

====Compact dimensions====
Two different ways have been proposed to resolve this apparent contradiction. The first is to [[Dimensional reduction|compactify]] the extra dimensions; i.e., the 6 or 7 extra dimensions are so small as to be undetectable by present day experiments.

To retain a high degree of supersymmetry, these compactification spaces must be very special, as reflected in their [[holonomy]]. A 6-dimensional manifold must have SU(3) structure, a particular case ([[torsion tensor|torsionless]]) of this being SU(3) holonomy, making it a [[Calabi-Yau space]], and a 7-dimensional manifold must have [[G2 manifold|G<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 4-dimensional [[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.

A standard analogy for this is to consider multidimensional space as a garden hose. If the hose is viewed from a 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 one-dimensional, 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 [[wave-particle duality]]).

====Brane-world scenario====
{{Unreferenced section|date=November 2008}}
Another possibility is that we are "stuck" in a 3+1 dimensional (i.e. three spatial dimensions plus the time dimension) subspace of the full universe. This subspace is supposed to be a [[D-brane]], hence this is known as a [[Brane cosmology|braneworld]] theory. Some believe that some combination of the two ideas — compactification and branes — will ultimately yield the most realistic theory.{{Citation needed|date=November 2007}}

====Effect of the hidden dimensions====
In either case, gravity acting in the hidden dimensions affects other non-gravitational 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 four-dimensional 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.

===D-branes===
{{Main|D-brane}}

Another key feature of string theory is the existence of D-branes. These are membranes of different dimensionality (anywhere from a zero dimensional membrane — which is in fact a point — and up, including 2-dimensional membranes, 3-dimensional volumes and so on).

D-branes are defined by the fact that [[worldsheet]] [[Boundary (topology)|boundaries]] are attached to them. Thus D-branes can emit and absorb closed strings; therefore they have mass (since they emit [[graviton]]s) and — in [[superstring theory|superstring theories]] — [[Charge (physics)|charge]] as well (since they emit closed strings which are gauge bosons).

From the point of view of open strings, D-branes are objects to which the ends of open strings are attached. The open strings attached to a D-brane are said to "live" on it, and they give rise to [[gauge theory|gauge theories]] "living" on it (since one of the open string modes is a [[gauge boson]] such as the photon). In the case of one D-brane there will be one type of a gauge boson and we will have an [[Abelian group|Abelian]] gauge theory (with the gauge boson being the [[photon]]). If there are multiple parallel D-branes there will be multiple types of gauge bosons, giving rise to a [[Non-abelian|non-Abelian]] gauge theory.

D-branes are thus gravitational sources, on which a gauge theory "lives". This gauge theory is [[Coupling (physics)|coupled]] to [[gravity]] (which is said to exist in the ''bulk''), so that normally each of these two different viewpoints is incomplete.

==Gauge-gravity duality==<!-- This section is linked from [[String theory]] -->
Gauge-gravity duality is a conjectured duality between a quantum theory of gravity in certain cases and [[gauge theory]] in a lower number of dimensions. This means that each predicted phenomenon and quantity in one theory has an analogue in the other theory, with a "dictionary" translating from one theory to the other.

===Description of the duality===
In certain cases the [[gauge theory]] on the D-branes is [[Coupling (physics)|decoupled]] from the [[gravity]] living in the bulk; thus open strings attached to the D-branes are not [[Fundamental interaction|interacting]] with closed strings. Such a situation is termed a ''decoupling limit''.

In those cases, the D-branes have two independent alternative descriptions. As discussed above, from the point of view of closed strings, the D-branes are gravitational sources, and thus we have a gravitational theory on spacetime with some background fields. From the point of view of open strings, the physics of the [[D-brane]]s is described by the appropriate gauge theory. Therefore in such cases it is often conjectured that the gravitational theory on spacetime with the appropriate background fields is dual (i.e. physically equivalent) to the gauge theory on the boundary of this spacetime (since the subspace filled by the D-branes is the boundary of this spacetime). So far, this duality has not been proven in any cases, so there is also disagreement among string theorists regarding how strong the duality applies to various models.

===Examples and intuition===
The most well-known example and the first one to be studied is the duality between Type IIB [[supergravity]] on ''AdS''<sup>''5''</sup> <math>\times</math> ''S''<sup>''5''</sup> 
(a [[product space]] of a five-dimensional [[Anti de Sitter space]] and a five-sphere) on one hand, and ''N'' = 4 [[supersymmetry|supersymmetric]] [[Yang-Mills theory]] on the four-dimensional boundary of the Anti de Sitter space (either a flat four-dimensional spacetime ''R''<sup>''3,1''</sup> or a three-[[sphere]] with time ''S''<sup>''3''</sup> <math>\times</math> ''R'').<ref>{{cite journal| title=Large N Field Theories, String Theory and Gravity| journal= Phys. Rept.| date=2000| volume=323| year=2000| pages= 183–386| doi=10.1016/S0370-1573(99)00083-6| arxiv=hep-th/9905111| last1=Aharony| first1=Ofer| last2=Gubser| first2=Steven S.| last3=Maldacena| first3=Juan| last4=Ooguri| first4=Hirosi| last5=Oz| first5=Yaron| issue=3–4}}. For other examples see: [[arXiv:hep-th/9802042]]</ref> This is known as the [[AdS/CFT correspondence]], a name often used for Gauge / gravity duality in general.

This duality can be thought of as follows: suppose there is a spacetime with a gravitational source, for example an [[extremal black hole]].<ref>Robbert Dijkgraaf,Erik Verlinde and Herman Verlinde(1997)"[http://arxiv.org/abs/hep-th/9704018v2 5D Black Holes and Matrix Strings]"</ref> When particles are far away from this source, they are described by closed strings (i.e. a gravitational theory, or usually [[supergravity]]). As the particles approach the gravitational source, they can still be described by closed strings; alternatively, they can be described by objects similar to [[QCD string]]s,<ref>Minoru Eto,Koji Hashimoto and Seiji Terashima(2007)"[http://arxiv.org/abs/0706.2005v1 QCD String as Vortex String in Seiberg-Dual Theory]"</ref><ref>Harvey B.Meyer(2005)"[http://arxiv.org/abs/hep-th/0506034v1 Vortices on the worldsheet of the QCD string]"</ref><ref>Koji Hashimoto(2007)"[http://www2.yukawa.kyoto-u.ac.jp/~kiasyk2/slides/hashimoto.pdf Cosmic Strings, ＱＣＤ Strings and D-branes]"</ref> which are made of [[gauge boson]]s ([[gluon]]s) and other [[gauge theory]] degrees of freedom.<ref>Piljin Yi(2007)"[http://www2.yukawa.kyoto-u.ac.jp/~gc2007/pdf/yi.pdf Story of baryons in a gravity dual of QCD]"</ref> So if one is able (in a ''decoupling limit'') to describe the gravitational system as two separate regions — one (the ''bulk'') far away from the source, and the other close to the source — then the latter region can also be described by a gauge theory on D-branes. This latter region (close to the source) is termed the ''near-horizon limit'', since usually there is an [[event horizon]] around (or at) the gravitational source.

In the gravitational theory, one of the directions in spacetime is the radial direction, going from the gravitational source and away (towards the bulk). The gauge theory lives only on the D-brane itself, so it does not include the radial direction: it lives in a spacetime with one less dimension compared to the gravitational theory (in fact, it lives on a spacetime identical to the boundary of the near-horizon gravitational theory). Let us understand how the two theories are still equivalent:

The physics of the near-horizon gravitational theory involves only [[on-shell]] states (as usual in string theory), while the [[field theory]] includes also [[off-shell]] [[correlation function]]. The on-shell states in the near-horizon gravitational theory can be thought of as describing only particles arriving from the bulk to the near-horizon region and interacting there between themselves. In the gauge theory these are "projected" onto the boundary, so that particles which arrive at the source from different directions will be seen in the gauge theory as (off-shell) quantum fluctuations far apart from each other, while particles arriving at the source from almost the same direction in space will be seen in the gauge theory as (off-shell) quantum fluctuations close to each other. Thus the angle between the arriving particles in the gravitational theory translates to the distance scale between quantum fluctuations in the gauge theory. The angle between arriving particles in the gravitational theory is related to the radial distance from the gravitational source at which the particles interact: the larger the angle, the closer the particles have to get to the source in order to interact with each other. On the other hand, the scale of the distance between quantum fluctuations in a [[quantum field theory]] is related (inversely) to the energy scale in this theory. So small radius in the gravitational theory translates to low energy scale in the gauge theory (i.e. the IR regime of the [[field theory]]) while large radius in the gravitational theory translates to high energy scale in the [[gauge theory]] (i.e. the UV regime of the field theory).

A simple example to this principle is that if in the gravitational theory there is a setup in which the [[dilaton]] field (which determines the strength of the [[Coupling (physics)|coupling]]) is decreasing with the radius, then its dual field theory will be [[Asymptotic freedom|asymptotically free]], i.e. its coupling will grow weaker in high energies.

===Contact with experiment===
This branch of string theory may lead to new insights on [[quantum chromodynamics]], a gauge theory which is the fundamental theory of the [[strong interaction|strong nuclear force]]. To this end, it is hoped that a gravitational theory dual to quantum chromodynamics will be found.<ref>For example: T. Sakai and S. Sugimoto, ''Low energy hadron physics in holographic QCD'', Prog.Theor.Phys.113:843-882,2005, [[arXiv:hep-th/0412141]], December 2004</ref>

In fact, a vague contact with experiment has already been claimed to have been achieved<ref name="autogenerated2" /><ref name="autogenerated1" /><ref name="autogenerated3" /><ref name="autogenerated4" />, though currently the alternative explanation for [[quark-gluon plasma]] behavior, [[Lattice QCD]], is doing a much better job and has already made contact with experiments in various fields with good results,<ref>See for example [http://www.physics.indiana.edu/~sg/milc/results.pdf Recent Results] of the MILC research program, taken from the [http://www.physics.indiana.edu/~sg/milc.html MILC Collaboration homepage]</ref> though the computations are [[Numerical analysis|numerical]] rather than [[Analytic solution|analytic]].
Other possible experiments for string theory have been proposed. One is the discovery of large cosmic strings in space, formed when the high energies in the Big Bang "stretched" some strings to astronomical proportions. Other possible avenues of experiment which could help provide evidence for string theory may take place at the newly built [[Large Hadron Collider]]. One is the measurement of the strength of gravity on a microscopic scale, which could provide evidence for extra dimensions; if gravitons (which are closed strings) leak off the membrane, at small scales the force of gravity should be much greater than at large scales where the gravitons would have ample chance to leak away into the bulk. The discovery of [[supersymmetry]] could also be considered evidence since string theory was the first theory to require it, though other theories have managed to incorporate supersymmetry as well. Also, the absence of supersymmetric particles at energies accessible to the LHC would not necessarily disprove string theory, since supersymmetry could exist but still be outside the accelerator's range.

{{unsolved|physics|Is there a string theory vacuum which exactly describes everything in our universe? Is it uniquely determined by low energy data?}}
==Problems and controversy==

Although string theory comes from physics, some say that string theory's current untestable status means that it should be classified as more of a mathematical framework for building models as opposed to a physical theory<ref>David Gross, [http://video.tau.ac.il/Lectures/Exact_Sciences/Physics/stringfest/OnDemand.html?11 Perspectives], String Theory: Achievements and Perspectives - A conference</ref>. 
Some go further, and say that string theory as a [[theory of everything]] is a failure.<ref name = "Wrong">[http://www.math.columbia.edu/~woit/wordpress/?cat=2 Peter Woit's ''Not Even Wrong'' weblog]</ref><ref name = "Smolin">[http://www.thetroublewithphysics.com Lee Smolin's ''The Trouble With Physics'' webpage]</ref> This led to a public debate in 2007<ref>e.g. John Baez and responses on the group weblog [http://golem.ph.utexas.edu/category/2007/02/this_weeks_finds_in_mathematic_7.html The n-Category Cafe]</ref><ref>[http://math.ucr.edu/home/baez/week246.html John Baez weblog]</ref>, with one commentator expressing this opinion:

<blockquote>"For more than a generation, physicists have been chasing a will-o’-the-wisp called string theory. The beginning of this chase marked the end of what had been three-quarters of a century of progress. Dozens of string-theory conferences have been held, hundreds of new Ph.D.s have been minted, and thousands of papers have been written. Yet, for all this activity, not a single new testable prediction has been made, not a single theoretical puzzle has been solved. In fact, there is no theory so far—just a set of hunches and calculations suggesting that a theory might exist. And, even if it does, this theory will come in such a bewildering number of versions that it will be of no practical use: a Theory of Nothing." -- Jim Holt.<ref>[http://www.newyorker.com/archive/2006/10/02/061002crat_atlarge Unstrung: The New Yorker]</ref> </blockquote>

=== Is string theory predictive? ===

String theory as a [[theory of everything]] has been criticized as unscientific because it is so difficult to test by experiments. The controversy centers around two properties:

#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>Elias Kiritsis(2007)"[http://press.princeton.edu/chapters/s8456.pdf String Theory in a Nutshell]"</ref> can reach.
# String theory as it is currently understood has a huge number of equally possible solutions, called string vacua<ref name = "KKLT">S. Kachru, R. Kallosh, A. Linde and S. P. Trivedi, ''de Sitter Vacua in String Theory'', Phys.Rev.D68:046005,2003, [[arXiv:hep-th/0301240]]</ref> and these vacua might be sufficiently diverse to explain almost any phenomena we might observe at lower energies.

If these properties are true, string theory as a theory of everything would have little or no [[predictive power]] for low energy particle physics experiments.<ref>P. Woit (Columbia University), ''String theory: An Evaluation'',February 2001, [[arXiv:physics/0102051]]</ref><ref>P. Woit, [http://www.math.columbia.edu/~woit/testable.pdf Is String Theory Testable?] INFN Rome March 2007</ref> Because the theory is so difficult to test, some theoretical physicists have asked if it can even be called a [[theory|scientific theory]]. Notable critics include [[Peter Woit]], [[Lee Smolin]], [[Philip Anderson]] <ref>"string theory is the first science in hundreds of years to be pursued in pre-Baconian fashion, without any adequate experimental guidance", [[New York Times]], 4 January 2005</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/view-glashow.html NOVA interview])</ref>,  [[Lawrence Krauss]] <ref> "String theory [is] yet to have any real successes in explaining or predicting anything measurable" [[New York Times]], 8 November 2005)</ref>, and [[Carlo Rovelli]].<ref>see his ''Dialog on Quantum Gravity'', [[arXiv:hep-th/0310077]])</ref> 

All string theory models are quantum mechanical, Lorentz invariant, unitary, and contain Einstein's [[General Relativity]] as a low energy limit.<ref>J. Polchinski, ''String Theory'', Cambridge University Press, Cambridge, UK (1998)</ref> So to falsify string theory, it suffices to falsify quantum mechanics, Lorentz invariance, or general relativity. Therefore string theory is falsifiable and meets the definition of [[scientific theory]] according to the [[Karl Popper|Popperian]] criterion.  However to constitute a convincing potential verification of string theory, a prediction should be specific to it, not shared by any quantum field theory model or by General Relativity.

One such unique prediction is ''string harmonics'': at sufficiently high energies—probably near the quantum gravity scale—the string-like nature of particles would become obvious. There should be heavier copies of all particles corresponding to higher vibrational states of the string. But it is not clear how high these energies are. In the most likely case, they would be 10<sup>15</sup> times higher than those accessible in the newest [[particle accelerator]], the [[Large Hadron Collider|LHC]], making this prediction impossible to test with a particle accelerator in the foreseeable future.

=== Swampland ===

In response to these concerns, [[Cumrun Vafa]] and others have challenged the idea that string theory is compatible with anything. They propose that most possible theories of low energy physics lie in the [[swampland (physics)|swampland]]. The swampland is the collection of theories which could be true if gravity wasn't an issue, but which are not compatible with string theory. An example of a theory in the swampland is quantum electrodynamics in the limit of very small electron charge. This limit is perfectly fine in quantum field theory — in fact, in this limit, the perturbation theory becomes better and better. But in string theory, at the moment the charge of the lightest charged particle becomes less than the mass in natural units, the theory becomes inconsistent.

The reason is that two such charged massive particles will attract each other gravitationally more than they repel each other electrostatically, and could be used to form black holes. If there are no light charged particles, these black holes could not decay efficiently, barring improbable conspiracies or remnants. From the study of examples, and from the analysis of black-hole evaporation,  it is now accepted that theories with a small charge quantum must come with light charged particles. This is only true within string theory—there is no such restriction in [[quantum field theory]]. This means that the discovery of a new gauge group with a small quantum of charge and only heavy charged particles would falsify string theory. Since this argument is very general—relying only on black-hole evaporation and the [[holographic principle]], it has been suggested that this prediction would be true of any consistent holographic theory of quantum gravity, although the phrase "consistent holographic theory of quantum gravity" might very well be synonymous with "string theory".

It is notable that all the gross features of the [[Standard model]] can be embedded within String theory, so that the standard model is not in the swampland. This includes features such as non-abelian gauge groups and chiral fermions which are hard to incorporate in non-string theories of quantum gravity.

=== Background independence ===
{{Main|Background independence}}
A separate and older criticism of string theory is that it is background-dependent — string theory describes perturbative expansions about fixed spacetime backgrounds. Although the theory has some background-independence — topology change is an established process in string theory, and the exchange of gravitons is equivalent to a change in the background — mathematical calculations in the theory rely on preselecting a background as a starting point. This is because, like many [[quantum field theory|quantum field theories]], much of string theory is still only formulated [[Perturbation theory (quantum mechanics)|perturbative]]ly, as a [[divergent series]] of approximations. Although nonperturbative techniques have progressed considerably — including conjectured complete definitions in [[spacetime]]s satisfying certain asymptotics — a full [[non-perturbative]] definition of the theory is still lacking. Some see background independence as a fundamental requirement of a theory of quantum gravity, particularly since [[General Relativity]] is already background independent. Some hope that [[M-theory]], or a [[non-perturbative]] treatment of string theory ([[string field theory]] was thought to be non-perturbative in the 1980s) have a background-independent formulation.

=== Supersymmetry breaking ===
{{Main|Supersymmetry}}
A central problem for applications is that the best understood backgrounds of string theory preserve much of the supersymmetry of the underlying theory, which results in time-invariant spacetimes: currently string theory cannot deal well with time-dependent, cosmological backgrounds. However, several models have been proposed to explain supersymmetry breaking, most notably the KKLT model<ref name="KKLT" />, which incorporates branes and fluxes to make a metastable compactification.

The vacuum structure of the theory, called the [[string theory landscape]], is not well understood. String theory contains an infinite number of distinct meta-stable vacua, and perhaps 10<sup>500</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.

Some physicists believe this is a good thing, because it may allow a natural [[anthropic principle|anthropic explanation]] of the observed values of [[physical constant]]s, in particular the small value of the [[cosmological constant]].<ref> N. Arkani-Hamed, S. Dimopoulos and S. Kachru, ''Predictive Landscapes and New Physics at a TeV'', [[arXiv:hep-th/0501082]], SLAC-PUB-10928, HUTP-05-A0001, SU-ITP-04-44, January 2005</ref><ref>L. Susskind ''The Anthropic Landscape of String Theory'', [[arXiv:hep-th/0302219]], February 2003</ref> The argument is that most universes contain values for physical constants which do not lead to habitable universes (at least for humans), and so we happen to live in the most "friendly" universe. This principle is already employed to explain the existence of life on earth as the result of a life-friendly orbit around the medium-sized sun among an infinite number of possible orbits (as well as a relatively stable location in the galaxy). However, the cosmological version of the anthropic principle remains highly controversial because it would be difficult if not impossible to [[Karl Popper|Popper]] [[falsification|falsify]]; so many do not accept it as scientific.

=== Other testability criteria ===

Many physicists strongly oppose the idea that string theory is not falsifiable, among them  [[Sylvester James Gates]]: "So, the next time someone tells you that string theory is not testable, remind them of the [[AdS/CFT]] connection ..."<ref>S. James Gates, Jr., Ph.D., Superstring Theory: The DNA of Reality "Lecture 21 - Can 4D Forces (without Gravity) Love Strings?", 0:26:06-0:26:21, cf. 0:24:05-0:26-24.</ref> [[AdS/CFT]] relates string theory to gauge theory, and allows contact with low energy experiments in [[quantum chromodynamics]]. This type of string theory, which only describes the strong interactions, is much less controversial today than string theories of everything (although two decades ago, it was the other way around).

In addition, Gates points out that the [[grand unified theory|grand unification]] natural in string theories of everything requires that the coupling constants of the four forces meet at one point under renormalization group rescaling. This is also a falsifiable statement, but it is not restricted to string theory, but is shared by [[grand unified theory|grand unified theories]].<ref>Idem, "Lecture 19 - Do-See-Do and Swing your Superpartner Part II" 0:16:05-0:24:29.</ref> The [[Large Hadron Collider|LHC]] will be used both for testing [[AdS/CFT]], and to check if the electroweakstrong unification does happen as predicted.<ref>Idem, Lecture 21, 0:20:10-0:21:20.</ref>

==Popular culture==

String theory has been the focus of several popular works:

* The book ''[[The Elegant Universe]]'' by [[Brian Greene]], Professor of Physics at [[Columbia University]], was adapted into a three-hour documentary for ''[[NOVA (TV series)|Nova]]'' and also shown on British television. It was also shown by [[Discovery Channel]] on [[Republic of India|Indian]] television, as well as in Australia on SBS, in [[Argentina]] in the channel Encuentro and in [[Iran]] in the channel Education.

In addition aspects of string theory are referenced in various contexts:

*'''Television''': ''[[Sliders]]'', ''[[The Big Bang Theory]]'' ([[Sheldon Cooper]]), ''[[Masters of Horror]]'' (ep. [[H.P. Lovecraft's Dreams in the Witch-House]]), [[CSI]] (ep. "The Theory of Everything"), [[The Suite Life Of Zack And Cody]] (ep. [[The Suite Smell of Excess]]),[[Quantum Leap (TV series)|Quantum Leap]] (Season 3, Ep. 13 "Future Boy")
*'''Books''': [[Ilium]] and [[Olympos]] by [[Dan Simmons]], [[River of Gods]] by [[Ian McDonald]]
*'''Music''': [[Lupe Fiasco]]'s [[Hurt Me Soul]]
*'''Comics''': [[Zippy the Pinhead]], [[xkcd]]<ref>."[http://xkcd.com/171/ XKCD:String Theory]</ref>

==See also==
{{Wiktionary|string theory}}
* [[List of string theory topics]]
*[[:Category:String theory physicists|List of string theory physicists]]

<div style="-moz-column-count:4; column-count:4;">
* [[AdS/CFT correspondence]]
* [[Conformal field theory]]
* [[Dual resonance model]]
* [[F-theory]]
* [[Fuzzballs]]
* [[Graviton]]
* [[Kaluza-Klein theory]]
* [[Loop quantum gravity]]
* [[M-theory]]
* [[Quantum gravity]]
* [[Relationship between string theory and quantum field theory]]
* [[String cosmology]]
* [[String duality]]
* [[String theory landscape]]
* [[Supergravity]]
* [[Superstring theory]]
* [[Supersymmetry]]
* [[Theory of everything]]
* [[Zeta function regularization]]
</div>

==References==
{{reflist|2}}

==Further reading==
===Popular books and articles===
* {{cite book | first = Paul | last = Davies | authorlink = Paul Davies | coauthors = Julian R. Brown (Eds.) | year = 1992 | month = July 31 | title = Superstrings: A Theory of Everything? | chapter =  | editor =  | edition = Reprint | pages = 244 | publisher = Cambridge University Press | location = Cambridge | isbn = 0-521-43775-X | url = }}
*{{cite web | author=Gefter, Amanda | title=''Is string theory in trouble?''  | publisher=[[New Scientist]] | date=December 2005 | year=2005 | url=http://www.newscientist.com/article/mg18825305.800-is-string-theory-in-trouble.html?full=true | accessdate=December 19, 2005}} – An interview with [[Leonard Susskind]], the theoretical physicist who discovered that string theory is based on one-dimensional objects and now is promoting the idea of [[Multiverse (science)|multiple universes]].
*{{cite web | author=[[Michael Green (physicist)|Green, Michael]] | title=''Superstrings''  | publisher=[[Scientific American]] | date=September 1986 | year=1986 | url=http://www.damtp.cam.ac.uk/user/mbg15/superstrings/superstrings.html | accessdate=December 19, 2005}}
* {{cite book | first = Brian | last = Greene | authorlink = Brian Greene | year = 2003 | month = October 20 | title = [[The Elegant Universe|The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory]] | chapter =  | editor =  | edition = Reissue | pages = 464 | publisher = W.W. Norton & Company | location = New York | isbn = 0-393-05858-1 | url = }}
* {{cite book | first = Brian | last = Greene | authorlink = Brian Greene | year = 2004 | title = [[The Fabric of the Cosmos: Space, Time, and the Texture of Reality]] | chapter =  | editor =  | edition = | pages = 569 | publisher = Alfred A. Knopf | location = New York | isbn = 0-375-41288-3 | url = }}
* {{cite book | first = John | last = Gribbin | authorlink = John Gribbin | year = 1998 | title = The Search for Superstrings, Symmetry, and the Theory of Everything | chapter =  | editor =  | edition =  | pages = 224 | publisher = Little Brown and Company | location = London | isbn = 0-316-32975-4 | url = }}
* {{cite book | first = Paul | last = Halpern | authorlink = Paul Halpern | year = 2004 | title = The Great Beyond: Higher Dimensions, Parallel Universes, and the Extraordinary Search for a Theory of Everything | chapter =  | editor =  | edition = | pages = 326 | publisher = John Wiley & Sons, Inc. | location = Hoboken, New Jersey | isbn = 0-471-46595-X | url = }}
* {{cite book | first = Dan | last = Hooper | authorlink = | year = 2006 | title = Dark Cosmos: In Search of Our Universe's Missing Mass and Energy | chapter =  | editor =  | edition = | pages = 240 | publisher = HarperCollins | location = New York | isbn = 978-0-06-113032-8 | url = }}
* {{cite book | first = Michio | last = Kaku | authorlink = Michio Kaku | year = 1994 | date = April 1994 | title = Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension | chapter =  | editor =  | edition =  | pages = 384 | publisher = Oxford University Press | location = Oxford | isbn = 0-19-508514-0 | url = }}
*[[Igor Klebanov|Klebanov, Igor]] and [[Juan Maldacena|Maldacena, Juan]] (January 2009). [http://ptonline.aip.org/journals/doc/PHTOAD-ft/vol_62/iss_1/28_1.shtml Solving Quantum Field Theories via Curved Spacetimes]. ''[[Physics Today]]''.
* {{cite book | first = George | last = Musser | authorlink = George Musser | year = 2008 | title = The Complete Idiot's Guide to String Theory | chapter =  | editor =  | edition = | pages = 368 | publisher = Alpha | location = Indianapolis | isbn = 978-1-59-257702-6 | url = }}
* {{cite book | first = Lisa | last = Randall | authorlink = Lisa Randall | year = 2005 | month = September 1 | title = [[Warped Passages]]: Unraveling the Mysteries of the Universe's Hidden Dimensions | chapter =  | editor =  | edition =  | pages = 512 | publisher = Ecco Press | location = New York | isbn = 0-06-053108-8 | url = }}
* {{cite book | first = Leonard | last = Susskind | authorlink = Leonard Susskind | year = 2006 | date = December 2006 | title = [[Leonard_Susskind#The_Cosmic_Landscape|The Cosmic Landscape]]: String Theory and the Illusion of Intelligent Design | chapter =  | editor =  | edition =  | pages = 403 | publisher = Hachette Book Group/Back Bay Books | location = New York | isbn = 0-316-01333-1 | url = }}
* [[Gary Taubes|Taubes, Gary]] (November 1986). "Everything's Now Tied to Strings" ''Discover Magazine'' vol 7, #11. (Popular article, probably the first ever written, on the [[first superstring revolution]].)
* {{cite book | first = Alex | last = Vilenkin | authorlink = Alex Vilenkin | year = 2006 | title = Many Worlds in One: The Search for Other Universes | chapter =  | editor =  | edition = | pages = 235 | publisher = Hill and Wang | location = New York | isbn = 0-8090-9523-8 | url = }}
*{{cite web | author=[[Edward Witten|Witten, Edward]] | title=''The Universe on a String'' | publisher=[[Astronomy Magazine]] | date=June 2002 | year=2002 | url=http://www.sns.ias.edu/~witten/papers/string.pdf | accessdate=December 19, 2005}} – An easy nontechnical article on the very basics of the theory.

Two nontechnical books that are critical of string theory:
* {{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 | chapter =  | editor =  | edition = | pages = 392 | publisher = Houghton Mifflin Co. | location = New York | isbn = 0-618-55105-0 | url = }}
* {{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 | chapter =  | editor =  | edition =  | pages = 290 | publisher = New York: Basic Books | location = London: Jonathan Cape &| isbn = 0-224-07605-1 & {{ISBN|978-0-465-09275-8}}}}

===Textbooks===
* Becker, Katrin, Becker, Melanie, and [[John H. Schwarz]] (2007) ''String Theory and M-Theory: A Modern Introduction ''. Cambridge University Press. {{ISBN|0-521-86069-5}}
* Binétruy, Pierre (2007) ''Supersymmetry: Theory, Experiment, and Cosmology''. Oxford University Press. {{ISBN|978-0-19-850954-7}}.
* Dine, Michael (2007) ''Supersymmetry and String Theory: Beyond the Standard Model''. Cambridge University Press. {{ISBN|0-521-85841-0}}.
*{{cite book | author=[[Paul Frampton|Paul H. Frampton]] |
title=Dual Resonance Models |
publisher=Frontiers in Physics |
year=1974 | isbn=0-805-32581-6}}
* Gasperini, Maurizio (2007) ''Elements of String Cosmology''. Cambridge University Press. {{ISBN|978-0-521-86875-4}}.
* [[Michael Green (physicist)|Michael Green]], [[John H. Schwarz]] and [[Edward Witten]] (1987) ''Superstring theory''. Cambridge University Press. The original textbook.
** ''Vol. 1: Introduction''. {{ISBN|0-521-35752-7}}.
** ''Vol. 2: Loop amplitudes, anomalies and phenomenology''. {{ISBN|0-521-35753-5}}.
* Kiritsis, Elias (2007) ''String Theory in a Nutshell''. Princeton University Press. {{ISBN|978-0-691-12230-4}}.
* {{cite book | first = Clifford | last = Johnson | year = 2003 | title = D-branes | chapter =  | editor =  | edition =  | pages =  | publisher = Cambridge University Press | location = Cambridge | isbn = 0-521-80912-6 | url = }}
* [[Joseph Polchinski|Polchinski, Joseph]] (1998) ''String Theory''. Cambridge University Press.
** ''Vol. 1: An introduction to the bosonic string''. {{ISBN|0-521-63303-6}}.
** ''Vol. 2: Superstring theory and beyond''. {{ISBN|0-521-63304-4}}.
* Szabo, Richard J. (Reprinted 2007) ''An Introduction to String Theory and D-brane Dynamics''. Imperial College Press. {{ISBN|978-1-86094-427-7}}.
* [[Barton Zwiebach|Zwiebach, Barton]] (2004) ''A First Course in String Theory''. Cambridge University Press. {{ISBN|0-521-83143-1}}. Contact author for errata.

Technical and critical:
* {{cite book | first = Roger | last = Penrose | authorlink = Roger Penrose | year = 2005 | month = February 22 | title = [[The Road to Reality]]: A Complete Guide to the Laws of the Universe | chapter =  | editor =  | edition =  | pages = 1136 | publisher = Knopf | location =  | isbn = 0-679-45443-8 | url = }}

==External links==
*[http://www.perimeterinstitute.ca/en/Outreach/What_We_Research/Superstring_Theory/ Superstring Theory] Perimeter Institute for Theoretical Physics
*{{cite web | author=Schwarz, Patricia | title=The Official String Theory Web Site | publisher= | year=1998 | url=http://superstringtheory.com/ | accessdate=December 16, 2005}}
*{{cite web | author=WGBH Educational Foundation | title=The Elegant Universe | publisher=PBS Online, NOVA | year=2003 | url=http://www.pbs.org/wgbh/nova/elegant/ | accessdate=December 16, 2005}} – A Three-Hour 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.
*{{cite web | author=[[Jan Troost|Troost, Jan]] | title=Beyond String Theory | publisher= | year=2002 | url=http://www.phys.ens.fr/~troost/beyondstringtheory/ | accessdate=July 13, 2009}} – A project by a string physicist explaining aspects of string theory to a broad audience.
*[http://www.mathpages.com/home/kmath632/kmath632.htm Dialogue on the Foundations of String Theory] at MathPages
*{{cite web | author=[[John M. Pierre|Pierre, John M.]] | title=Superstrings! String Theory Home Page | publisher= | year=1999 | url=http://www.sukidog.com/jpierre/strings/ | accessdate=December 16, 2005}} – Online tutorial.
*{{cite web | author=[[Lubos Motl|Motl, Luboš]]; Screiber, Urs | title=SCI.physics. STRINGS newsgroup | publisher=Harvard High Energy Theory Group | year= | url=http://schwinger.harvard.edu/~sps/ | accessdate=December 16, 2005}} – A moderated newsgroup for discussion of string theory (a theory of quantum gravity and unification of forces) and related fields of high-energy physics.
*{{cite arXiv | author=[[John H. Schwarz|Schwarz, John H.]] | title=Introduction to Superstring Theory | year=2000 | work= | eprint=hep-ex/0008017 }} – Four lectures, presented at the [[NATO]] Advanced Study Institute on Techniques and Concepts of High Energy Physics, [[St. Croix]], [[Virgin Islands]], in June 2000, and addressed to an audience of graduate students in experimental [[high energy physics]], survey basic concepts in string theory.
*{{cite web | author=[[Edward Witten|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}} – Slides and audio from an Ed Witten lecture where he introduces string theory and discusses its challenges.
*{{cite arXiv | author=[[Tom W. B. Kibble|Kibble, Tom]] | title=Cosmic strings reborn? | year=2004 | work= | eprint=astro-ph/0410073 }} – Invited Lecture at COSLAB 2004, held at Ambleside, Cumbria, United Kingdom, from 10 to [[17 September]] [[2004]].
*{{cite journal | author=Marolf, Don | title=Resource Letter NSST-1: The nature and status of string theory | journal=American Journal of Physics | year=2004 | volume=72 | issue=6 | pages=730–741 | doi=10.1119/1.1736005 | arxiv=hep-th/0311044 }} – A guide to the string theory literature.
*{{cite web | author=Ajay, Shakeeb, Wieland et al. | title=The nth dimension | publisher= | year=2004 | url=http://thenthdimension.com/ | accessdate=December 16, 2005}} – A comprehensive compilation of materials concerning string theory. Created by an international team of students.
*{{cite web | author=[[Peter Woit|Woit, Peter]] | title=''Is string theory even wrong?'' | publisher=[[American Scientist]] | year=2002 | url=http://www.americanscientist.org/issues/pub/is-string-theory-even-wrong | accessdate=December 16, 2005}} – A criticism of string theory.
*{{cite web | author=[[Peter Woit|Woit, Peter]] | title=Not Even Wrong | publisher=Columbia University Mathematics Department | year=2004 | url=http://www.math.columbia.edu/~woit/blog/ | accessdate=December 16, 2005}} – A blog critical of string theory.
*{{Citation| last=Veneziano| first=Gabriele| author-link=Gabriele Veneziano| title=The Myth of the Beginning of Time| magazine=[[Scientific American]]| volume=| issue=| pages=| date=May 2004 |url=http://www.sciam.com/article.cfm?chanID=sa006&articleID=00042F0D-1A0E-1085-94F483414B7F0000
 }}
* {{Citation| last=McKie| first=Robin| author-link=| title=Setback as string theory of the universe is de-bunked| newspaper=[[The Hindu]]| date= 2006-10-09 | url=http://www.hindu.com/thehindu/holnus/008200610091240.htm| format={{Dead link|date=February 2009}} &ndash; <sup>[http://scholar.google.co.uk/scholar?hl=en&lr=&q=author%3AMcKie+intitle%3ASetback+as+string+theory+of+the+universe+is+de-bunked&as_publication=&as_ylo=&as_yhi=&btnG=Search Scholar search]</sup>}}
*{{cite web| last = Harris| first = Richard| title = Short of 'All,' String Theorists Accused of Nothing| publisher = National Public Radio| date = 2006-11-07 | url = http://www.npr.org/templates/story/story.php?storyId=6377252| format =| doi =| accessdate = 2007-03-05 }}
*[http://banyancollege.org/scriblerus/ A website dedicated to creative writing inspired by string theory.]
*{{cite newsgroup | title = Theory of everything put to the test| author = George Gardner| date = 2007-01-24 | newsgroup = tech.blorge.com| id = ID109828243| url = http://tech.blorge.com/Structure:%20/2007/01/24/theory-of-everything-put-to-the-test/| accessdate = 2007-03-03 }}
*{{Citation| last=Minkel| first=J. R.| author-link=| title=A Prediction from String Theory, with Strings Attached| magazine=[[Scientific American]]| date= 2006-03-02 | url=http://www.sciam.com/article.cfm?chanId=sa003&articleId=1475A684-E7F2-99DF-355B95296BE6031C}}
*{{cite web | author=[[Matthew Chalmers|Chalmers, Matthew]] | title=''Stringscape'' | publisher=[http://physicsworld.com Physics World] | date=2007-09-03 | url=http://physicsworld.com/cws/article/indepth/30940 | accessdate=September 6, 2007}} — An up-to-date and thorough review of string theory in a popular way.
* Smolin, Lee. The Trouble With Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next (2006), Houghton Mifflin. {{ISBN|978-0-618-55105-7}}.
* Woit, Peter. Not Even Wrong: The Failure of String Theory & the Continuing Challenge to Unify the Laws of Physics, 2006. {{ISBN|0-224-07605-1}} (Jonathan Cape), {{ISBN|0-465-09275-6}} (Basic Books)
*{{cite web | author=Zapata Marin, Oswaldo | title=Spinning the Superweb: Essays on the History of Superstring Theory | publisher= | year=2009 | url=http://www.spinningthesuperweb.blogspot.com | accessdate=June 15, 2009}}
</div>
*{{cite web | author=Shwarz, John | title=Early History of String Theory: A Personal Perspective | publisher= | year=2001 | url=http://online.itp.ucsb.edu/online/colloq/schwarz1/ | accessdate=July 17, 2009}}

{{DEFAULTSORT:String Theory}}