String theory

Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theory

String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects (strings) rather than the zero-dimensional points (particles) that are the basis of the Standard Model of particle physics. For this reason, string theories are able to avoid problems associated with the presence of point like particles in theories of physics, in particular the problem of defining a sensible quantum theory of gravity. Studies of string theories have revealed that they predict not just strings, but also higher-dimensional objects.

Overview

The basic idea behind all string theories is that the fundamental constituents of reality are strings of energy of the Planck length (about 10^-35 m) which vibrate at specific resonant frequencies. Thus any particle should be thought of as a tiny vibrating object, rather than as a point. A key consequence of the theory is that there is no operational way to probe distances shorter than the string length.

In addition to strings, string theories also include objects of higher dimensions, such as D-branes and NS-branes. Furthermore, all string theories predict the existence of degrees of freedom which are usually described as extra dimensions.

Interest in string theory is driven largely by the hope that it will prove to be a theory of everything. Indeed, much of the interest in string theory arose when physicists realized that quantum gravity was required for the theory's consistency. It can also naturally describe interactions similar to electromagnetism and the other forces of nature. Superstring theories include fermions, the building blocks of matter, and incorporate supersymmetry, a conjectured (but unobserved) symmetry of nature. It is not yet known whether string theory will be able to describe a universe with the precise collection of forces and particles that is observed, nor how much freedom to choose those details that the theory will allow, but much progress has been made in this direction.

However, string theory as a whole has not yet made falsifiable predictions that would allow it to be experimentally tested, though various planned observations and experiments could confirm some essential aspects of the theory, such as supersymmetry and extra dimensions. In addition, the full theory is not yet understood. For example, the theory does not yet have a satisfactory definition outside of perturbation theory, the quantum mechanics of branes (higher dimensional objects than strings) is not understood, and the behavior of string theory in cosmological settings (time-dependent backgrounds) is still being worked out. Finally, the principle by which string theory selects its vacuum state is a hotly contested topic (see string theory landscape).

History

String theory was originally invented to explain some peculiarities of the behavior of hadrons (subatomic particles which experiences the strong nuclear force). In particle-accelerator experiments, physicists observed that the spin of a hadron is never larger than a certain multiple of the square of its energy. No simple model of the hadron, such as picturing it as a set of smaller particles held together by spring-like forces, was able to explain these relationships. In 1968, theoretical physicist Gabriele Veneziano produced a model of the strong force that used the Euler Beta function as a scattering amplitude (the so-called Veneziano amplitude). While this provided a good fit to experimental data, the reasons for this fit were unknown.

In 1970, Yoichiro Nambu, Holger Bech Nielsen, and Leonard Susskind presented a physical interpretation of Euler's formula by representing nuclear forces as vibrating, one-dimensional strings. However, this string-based description of the strong force made many predictions that directly contradicted experimental findings. The scientific community soon lost interest in string theory, and the standard model, with its particles and fields, remained the main focus of theoretical research.

In 1974 John Schwarz and Joel Scherk, and independently Tamiaki Yoneya, studied the boson-like patterns of string vibration and found that their properties exactly matched those of the graviton, the gravitational force's hypothetical "messenger" particle. Schwarz and Scherk argued that string theory had failed to catch on because physicists had underestimated its scope. This led to the development of bosonic string theory, which is still the version first taught to many students. The original need for a viable theory of hadrons has been fulfilled by quantum chromodynamics, the theory of quarks and their interactions. It is now hoped that string theory or some descendant of it will provide a fundamental understanding of the quarks themselves.

String theory is formulated in terms of the Polyakov action, which describes how strings move through space and time. Like springs, the strings want to contract to minimize their potential energy, but conservation of energy prevents them from disappearing, and instead they oscillate. By applying the ideas of quantum mechanics to strings it is possible to deduce the different vibrational modes of strings, and that each vibrational state appears to be a different particle. The mass of each particle, and the fashion with which it can interact, are determined by the way the string vibrates — in essence, by the "note" which the string sounds. The scale of notes, each corresponding to a different kind of particle, is termed the "spectrum" of the theory.

Early models included both open strings, which have two distinct endpoints, and closed strings, where the endpoints are joined to make a complete loop. The two types of string behave in slightly different ways, yielding two spectra. Not all modern string theories use both types; some incorporate only the closed variety.

The earliest string model, which incorporated only bosons, has problems. Most importantly, the theory has a fundamental instability, believed to result in the decay of space-time itself. Additionally, as the name implies, the spectrum of particles contains only bosons, particles like the photon which obey particular rules of behavior. While bosons are a critical ingredient of the Universe, they are not its only constituents. Investigating how a string theory may include fermions in its spectrum led to the invention supersymmetry, a mathematical relation between bosons and fermions. String theories which include fermionic vibrations are now known as superstring theories; several different kinds have been described.

Between 1984 and 1986, physicists realized that string theory could describe all elementary particles and interactions between them, and hundreds of them started to work on string theory as the most promising idea to unify theories of physics. This first superstring revolution was started by a discovery of anomaly cancellation in type I string theory by Michael Green and John Schwarz in 1984. The anomaly is cancelled due to the Green-Schwarz mechanism. Several other ground-breaking discoveries, such as the heterotic string, were made in 1985.

File:Witten.jpg

Edward Witten

In the 1990s, Edward Witten and others found strong evidence that the different superstring theories were different limits of a new 11-dimensional theory called M-theory. These discoveries sparked the second superstring revolution.

In the mid 1990s, Joseph Polchinski discovered that the theory requires the inclusion of higher-dimensional objects, called D-branes. These added an additional rich mathematical structure to the theory, and opened many possibilities for constructing realistic cosmological models in the theory.

In 1997 Juan Maldacena conjectured a relationship between string theory and a gauge theory called N=4 supersymmetric Yang-Mills theory. This conjecture, called the AdS/CFT correspondence has generated a great deal of interest in the field and is now well accepted. It is a concrete realization of the holographic principle, which has far-reaching implications for black holes, locality and information in physics, as well as the nature of the gravitational interaction.

Most recently, the discovery of the string theory landscape, which suggests that string theory has an exponentially large number of inequivalent vacua, has led to much discussion of what string theory might eventually be expected to predict, and how cosmology can be incorporated into the theory.

Basic properties

While understanding the details of string and superstring theories requires considerable mathematical sophistication, some qualitative properties of quantum strings can be understood in a fairly intuitive 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 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

Imagine a point-like particle. If we draw a graph which depicts the progress of the particle as time passes by, the particle will draw a line in space-time. This line is called the particle's worldline. Now imagine a similar graph depicting the progress of a string as time passes by; the string (a one-dimensional object - a small line - by itself) will draw 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 closed string looks like a small loop, so its worldsheet will look like a pipe, or - more generally - as a Riemannian manifold (a two-dimensional oriented surface) 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 - as a Riemannian manifold with a boundary.

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 (see drawing at the top of this page). 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 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. 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.

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 and string in some version of the 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 an unoriented surface.

For details, see Relationship between string theory and quantum field theory.

Dualities

Before the "duality revolution" there were believed to be five distinct versions of string theory, plus the (unstable) bosonic theory.

String Theories
Type	Spacetime dimensions	Details
Bosonic	26	Only bosons, no fermions means only forces, no matter, with both open and closed strings; major flaw: a particle with imaginary mass, called the tachyon, representing an instability in the theory.
I	10	Supersymmetry between forces and matter, with both open and closed strings, no tachyon, group symmetry is SO(32)
IIA	10	Supersymmetry between forces and matter, with closed strings and open strings bound to D-branes, no tachyon, massless fermions spin both ways (nonchiral)
IIB	10	Supersymmetry between forces and matter, with closed strings and open strings bound to D-branes, no tachyon, massless fermions only spin one way (chiral)
HO	10	Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry is SO(32)
HE	10	Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry is E8×E8

Note that in the type IIA and type IIB string theories closed strings are allowed to move everywhere throughout the ten-dimensional space-time (called the bulk), while open strings have their ends attached to D-branes, 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).

Before the 1990s, string theorists believed there were five distinct superstring theories: type I, types IIA and IIB, and the two heterotic string theories (SO(32) and E₈×E₈). The thinking was that out of these five candidate theories, only one was the actual correct theory of everything, and that theory was the theory whose low energy limit, with ten dimensions spacetime compactified down to four, matched the physics observed in our world today. It is now known that this picture was naive, and that the five superstring theories are connected to one another as if they are each a special case of some more fundamental 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 two mathematically different descriptions of the same phenomena.

These dualities link quantities that were also thought to be separate. Large and small distance scales, strong and weak coupling strengths – these quantities 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.

Suppose we're in ten spacetime dimensions, which means we have nine space and one time. Take one of those nine space dimensions and make it a circle of radius R, so that traveling in that direction for a distance L = 2πR takes you around the circle and brings you back to where you started. A particle traveling around this circle will have a quantized momentum around the circle, because its momentum is linked to its wavelength (see Wave-particle duality), and 2πR must be a multiple of that. In fact, the particle momentum around the circle - and the contribution to its energy - is of the form n/R (in standard units, for an integer n), so that at large R there will be many more states compared to small R (for a given maximum energy). A string, in addition to traveling around the circle, may also wrap around it. The number of times the string winds around the circle is called the winding number, and that is also quantized (as it must be an integer). Winding around the circle requires energy, because the string must be streched against its tension, so it contributes an amount of energy of the form $wR/L_{st}^{2}$, where $L_{st}$ is the string length and w is the winding number (an integer). Now (for a given maximum energy) there will be many different states (with different momenta) at large R, but there will also be many different states (with different windings) at small R. In fact, a theory with large R and a theory with small R are equivalent, where the role of momentum in the first is played by the winding in the second, and vice versa. Mathematically, taking R to $L_{st}^{2}/R$ and switching n and w will yield the same equations. So exchanging momentum and winding modes of the string exchanges a large distance scale with a small distance scale.

This type of duality is called T-duality. T-duality relates type IIA superstring theory to type IIB superstring theory. That means if we take type IIA and Type IIB theory and compactify them both on a circle, then switching the momentum and winding modes, and switching the distance scale, changes one theory into the other. The same is also true for the two heterotic theories. T-duality also relates type I superstring theory to both type IIA and type IIB superstring theories with certain boundary conditions (termed orientifold).

Formally, the location of the string on the circle is described by two fields living on it, one which is left-moving and another which is right-moving. The movement of the string center (and hence its momentum) is related to the sum of the fields, while the string stretch (and hence its winding number) is related to their difference. T-duality can be formally described by taking the left-moving field to minus itself, so that the sum and the difference are interchanged, leading to switching of momentum and winding.

On the other hand, every force has a coupling constant, which is a measure of its strength, and determines the chances of one particle to emit or receive another particle. For electromagnetism, the coupling constant is proportional to the square of the electric charge. When physicists study the quantum behavior of electromagnetism, they can't solve the whole theory exactly, because every particle may emit and receive many other particles, which may also do the same, endlessly. So events of emission and reception are considered as perturbations and are dealt with by a series of approximations, first assuming there is only one such event, then correcting the result for allowing two such events, etc (this method is called Perturbation theory). This is a reasonable approximation only if the coupling constant is small, which is the case for electromagnetism. But if the coupling constant gets large, that method of calculation breaks down, and the little pieces become worthless as an approximation to the real physics.

This also can happen in string theory. String theories have a coupling constant. But unlike in particle theories, the string coupling constant is not just a number, but depends on one of the oscillation modes of the string, called the dilaton. Exchanging the dilaton field with minus itself exchanges a very large coupling constant with a very small one. This symmetry is called S-duality. If two string theories are related by S-duality, then one theory with a strong coupling constant is the same as the other theory with weak coupling constant. The theory with strong coupling cannot be understood by means of perturbation theory, but the theory with weak coupling can. So if the two theories are related by S-duality, then we just need to understand the weak theory, and that is equivalent to understanding the strong theory.

Superstring theories related by S-duality are: type I superstring theory with heterotic SO(32) superstring theory, and type IIB theory with itself.

Extra dimensions

File:Calabi-Yau art.jpg

An artist's impression of a Calabi-Yau manifold.

One intriguing feature of string theory is that it predicts the number of dimensions which the universe should possess. Nothing in Maxwell's theory of electromagnetism or Einstein's theory of relativity makes this kind of prediction; these theories require physicists to insert the number of dimensions "by hand". The first person to add a fifth dimension to Einstein's general relativity was German mathematician Theodor Kaluza in 1919. The reason for the unobservability of the fifth dimension (its compactness) was suggested by the Swedish physicist Oskar Klein in 1926.

Unlike general relativity, string theory allows one to compute the number of spacetime dimensions from first principles. Technically, this happens because for a different number of dimensions, the theory has a gauge anomaly. This can be understood by noting that in a consistent theory which includes a photon (technically, a particle carrying a force related to an unbroken gauge symmetry), it must be 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 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 will be massless — and the theory consistent — only for a particular number of dimensions.

When the calculation is done, the universe's dimensionality is not four as one may expect (three axes of space and one of time). Bosonic string theories are 26-dimensional, while superstring and M-theories turn out to involve 10 or 11 dimensions. In bosonic string theories, the 26 dimensions come from the Polyakov equation. However, these results appear to contradict the observed four dimensional space-time.

File:Calabi-Yau.jpeg

Calabi-Yau manifold (3D projection)

Two different ways have been proposed to resolve this apparent contradiction. The first is to compactify the extra dimensions; i.e., the 6 or 7 extra dimensions are so small as to be undetectable in our phenomenal experience. In order to retain the supersymmetric properties of string theory, these spaces must be very special. The 6-dimensional model's resolution is achieved with Calabi-Yau spaces. In 7 dimensions, they are termed G₂ manifolds. These extra dimensions are compactified by causing them to loop back upon themselves.

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 small enough to enter the hose - but not too small. 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 wave lengths (of the order of the compact dimension's radius), which in quantum mechanics means very high energies (see wave-particle duality).

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 braneworld theory. Many people believe that some combination of the two ideas – compactification and branes – will ultimately yield the most realistic theory.

In either case, gravity acting in the hidden dimensions affects other non-gravitational forces such as electromagnetism. In fact, Kaluza and Klein's early work demonstrated that general relativity with five large dimensions and one small dimension actually predicts the existence of electromagnetism. However, because of the nature of Calabi-Yau manifolds, 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.

Unsolved problem in physics:

Is string theory, superstring theory, or M-theory, or some other variant on this theme, a step on the road to a "theory of everything," or just a blind alley?

(more unsolved problems in physics)

Problems

String theory remains to be verified. No version of string theory has yet made a prediction which differs from those made by other theories — at least, not in a way that could be checked by a currently feasible experiment. In this sense, string theory is still in a "larval stage": it is properly a mathematical theory but is not yet a physical theory. It possesses many features of mathematical interest and may yet become supremely important in our understanding of the universe, but it requires further developments before it is accepted or falsified. Since string theory may not be tested in the foreseeable future, some scientists have asked if it even deserves to be called a scientific theory: it is not yet falsifiable in the sense of Popper.

For example, while supersymmetry is now seen as a vital ingredient of string theory, supersymmetric models with no obvious connection to string theory are also studied. Therefore, if supersymmetry were detected at the Large Hadron Collider it would not be seen as a direct confirmation of the theory. More importantly, if supersymmetry were not detected, there are vacua in string theory in which supersymmetry would only be seen at much higher energies, so its absence would not falsify string theory. By contrast, if observing the Sun during a solar eclipse had not shown that the Sun's gravity deflected light, Einstein's general relativity theory would have been proven wrong.

One hope for testing string theory is that a better understanding of how string theory deals with singularities and time-dependent backgrounds would allow physicists to understand the predictions of string theory for the big bang, and see how cosmic inflation can be incorporated into the theory. This has led to some deep theoretical progress, and some early models of string cosmology, such as brane inflation, trans-Planckian effects, string gas cosmology and the ekpyrotic universe, but fundamental progress must be made before it is understood what, if any, distinctive predictions the theory makes for cosmology. A recent popular suggestion is that brane inflation may produce cosmic strings which could be observed through their gravitational radiation, or lensing of distant galaxies or the cosmic microwave background.

On a more mathematical level, another problem is that, like many quantum field theories, much of string theory is still only formulated perturbatively (i.e., as a series of approximations rather than as an exact solution). Although nonperturbative techniques have progressed considerably – including conjectured complete definitions in space-times satisfying certain asymptotics – a full non-perturbative definition of the theory is still lacking.

Another problem is that the vacuum structure of the theory, called the string theory landscape, is not well understood. As string theory is presently understood, it appears to contain an exponentially large number of distinct vacua, perhaps 10⁵⁰⁰ or more. Each of these corresponds to a different universe, with a different collection of particles and forces. What principle, if any, can be used to select among these vacua is not widely agreed upon. While there are no known continuous parameters in the theory, there is a very large discretuum (coined in contradistinction to continuum) of possible universes, which may be radically different from each other. Some physicists believe this is a benefit of the theory, as it may allow a natural anthropic explanation of the observed small value of the cosmological constant.

Popular culture

The book The Elegant Universe by Brian Greene, Professor of Physics at Columbia University, was adapted into a three-hour documentary for Nova and also shown on British television. It was also shown by Discovery Channel on Indian television.

String theory is also a series of books based in the Star Trek: Voyager universe.

In the TV series Angel, the character of Winifred Burkle (aka Fred) puts forward a theory about String Theory & Alternate Dimensions to the Physics Institute following her own experience of being trapped in one such delicate alternate dimension for five years. The episode which this is referenced to is "Supersymmetry".

A theory named string theory was used in the science fiction television series Quantum Leap. In the series it relates to a theory of time travel. It views a person's life as a string that moves from one end to the other. However, if it were possible to roll up this string into a ball it would be possible to leap from one section to another. This was the explanation given to the time travelling occurring in the series.

See also

• List of string theory topics
• Kaluza-Klein theory
• Superstring theory
• M-theory
• F-theory
• Conformal field theory
• Graviton
• Quantum gravity
• AdS/CFT correspondence
• Loop quantum gravity
• Supergravity
• Supersymmetry
• Theory of everything
• Relationship between string theory and quantum field theory

References and further reading

Popular books and articles

• Davies, Paul (1992). Superstrings: A Theory of Everything? (Reprint edition ed.). Cambridge: Cambridge University Press. p. 244. ISBN 0-521-43775-X. {{cite book}}: |edition= has extra text (help); Unknown parameter |coauthors= ignored (|author= suggested) (help); Unknown parameter |month= ignored (help)
• Gefter, Amanda (December 2005). "Is string theory in trouble?". New Scientist. Retrieved December 19. {{cite web}}: Check date values in: |accessdate= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help)CS1 maint: year (link) – 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 multiple universes.
• Green, Michael (September 1986). "Superstrings". Scientific American. Retrieved December 19. {{cite web}}: Check date values in: |accessdate= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help)CS1 maint: year (link)
• Greene, Brian (2003). The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory (Reissue edition ed.). New York: W.W. Norton & Company. p. 464. ISBN 0-393-05858-1. {{cite book}}: |edition= has extra text (help); Cite has empty unknown parameter: |coauthors= (help); Unknown parameter |month= ignored (help)
• Gribbin, John (1998). The Search for Superstrings, Symmetry, and the Theory of Everything. London: Little Brown and Company. p. 224. ISBN 0-316-32975-4. {{cite book}}: Cite has empty unknown parameters: |coauthors= and |month= (help)
• Kaku, Michio (1994). Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension. Oxford: Oxford University Press. p. 384. ISBN 0-195-08514-0. {{cite book}}: Cite has empty unknown parameter: |coauthors= (help); Unknown parameter |month= ignored (help)
• Penrose, Roger (2005). The Road to Reality: A Complete Guide to the Laws of the Universe. Knopf. p. 1136. ISBN 0-679-45443-8. {{cite book}}: Cite has empty unknown parameter: |coauthors= (help); Unknown parameter |month= ignored (help)
• Randall, Lisa (2005). Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions. New York: Ecco Press. p. 512. ISBN 0-060-53108-8. {{cite book}}: Cite has empty unknown parameter: |coauthors= (help); Unknown parameter |month= ignored (help)
• Witten, Edward (June 2002). "The Universe on a String" (PDF). Astronomy magazine. Retrieved December 19. {{cite web}}: Check date values in: |accessdate= (help); External link in |publisher= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help)CS1 maint: year (link) – An easy article for everybody outside physics wanting to understand the very basics of the theory.

Textbooks

• Green, Michael, John 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.
• Johnson, Clifford (2003). D-branes. Cambridge: Cambridge University Press. ISBN 0-521-80912-6. {{cite book}}: Cite has empty unknown parameters: |coauthors= and |month= (help)
• Kaku, Michio (1998). Introduction to Superstrings and M-Theory (Second Edition ed.). New York: Springer-Verlag. pp. 612pp. ISBN 0-387-98589-1. {{cite book}}: |edition= has extra text (help); Cite has empty unknown parameters: |coauthors= and |month= (help)
• Polchinski, Joseph (1998). String Theory, Cambridge University Press. A modern textbook.
  • Vol. 1: An introduction to the bosonic string. ISBN 0-521-63303-6.
  • Vol. 2: Superstring theory and beyond. ISBN 0-521-63304-4.
• Zwiebach, Barton (2004). A First Course in String Theory, Cambridge University Press. ISBN 0-521-83143-1. Errata are available online.

External links

• Schwarz, Patricia (1998). "The Official String Theory Web Site". Retrieved December 16. {{cite web}}: |author= has generic name (help); Check date values in: |accessdate= (help); External link in |author= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help)
• WGBH Educational Foundation (2003). "The Elegant Universe". PBS Online, NOVA. Retrieved December 16. {{cite web}}: Check date values in: |accessdate= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help) – 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.
• Troost, Jan (2002). "Beyond String Theory". Vrije Universiteit Brussel, Theoretical Physics (TENA). Retrieved December 16. {{cite web}}: Check date values in: |accessdate= (help); External link in |author= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help) – An ongoing project by a string physicist, working for the French CNRS.
• Pierre, John M. (1999). "Superstrings! String Theory Home Page". Retrieved December 16. {{cite web}}: Check date values in: |accessdate= (help); External link in |author= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help) – Online tutorial.
• Frost, Clay (1999). "The Symphony of Everything". Retrieved December 16. {{cite web}}: Check date values in: |accessdate= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help) – A short interactive introduction to string theory based on Michio Kaku's "Beyond Einstein" (Microsoft Encarta Encyclopedia article).
• Motl, Luboš (2004). "Luboš Motl's reference frame". Blogger. Retrieved December 16. {{cite web}}: Check date values in: |accessdate= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help) – A blog supporting string theory.
• Motl, Luboš; Screiber, Urs. "SCI.physics. STRINGS newsgroup". Harvard High Energy Theory Group. Retrieved December 16. {{cite web}}: Check date values in: |accessdate= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help)CS1 maint: multiple names: authors list (link) – A moderated newsgroup for discussion of string theory (a theory of quantum gravity and unification of forces) and related fields of high-energy physics.
• Schwarz, John H. (2000). "Introduction to Superstring Theory". arXiv.org e-Print archive. Retrieved December 22. {{cite web}}: Check date values in: |accessdate= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help) – 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.
• Witten, Edward (1998). "Duality, Spacetime and Quantum Mechanics". Kavli Institute for Theoretical Physics. Retrieved December 16. {{cite web}}: Check date values in: |accessdate= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help) – Slides and audio from an Ed Witten lecture where he introduces string theory and discusses its challenges.
• Kibble, Tom (2004). "Cosmic strings reborn?". arXiv.org e-Print archive. Retrieved December 16. {{cite web}}: Check date values in: |accessdate= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help) – Invited Lecture at COSLAB 2004, held at Ambleside, Cumbria, United Kingdom, from 10 to 17 September 2004.
• Marolf, Don (2004). "Resource Letter NSST-1: The Nature and Status of String Theory". arXiv.org e-Print archive. Retrieved December 16. {{cite web}}: Check date values in: |accessdate= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help) – A guide to the string theory literature.
• Ajay, Shakeeb, Wieland; et al. (2004). "The nth dimension". Retrieved December 16. {{cite web}}: Check date values in: |accessdate= (help); Explicit use of et al. in: |author= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help)CS1 maint: multiple names: authors list (link) – A comprehensive compilation of materials concerning string theory. Created by an international team of students.
• Woit, Peter (2002). "Is string theory even wrong?". American Scientist. Retrieved December 16. {{cite web}}: Check date values in: |accessdate= (help); External link in |publisher= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help) – A criticism of string theory.
• Woit, Peter (2004). "Not Even Wrong". Columbia University Mathematics Department. Retrieved December 16. {{cite web}}: Check date values in: |accessdate= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help) – A blog critical of string theory.
• Has string theory tied up better ideas in physics?, Northwest Florida Daily News, 6/23/2006
• Scientific American Magazine (May 2004 Issue) The Myth of the Beginning of Time Time and String Theory.