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String theory

String theory is an as-yet incomplete mathematical approach to theoretical physics, whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point particles that form the basis for the standard model of particle physics. By replacing the point-like particles with strings, an apparently consistent quantum theory of gravity emerges, which has not been achievable under the standard model. Usually, the term string theory includes a group of related superstring theories and a few related frameworks such as M-theory, which seeks to unite them all.

String theorists have not yet completely described these theories, or determined if or how these theories relate to the physical universe. The elegance and flexibility of the approach, however, and a number of qualitative similarities with more traditional physical models, have led many physicists to suspect that such a connection is possible. In particular, string theory may be a way to "unify" the known natural forces (gravitational, electromagnetic, weak nuclear and strong nuclear) by describing them with the same set of equations, as described in the theory of everything. On the other hand, the models have been criticized for their inability, thus far, to provide any testable predictions.

Work on string theory is made difficult by the very complex mathematics involved, and the large number of forms that the theories can take depending on the arrangement of space and energy. Thus far, string theory strongly suggests the existence of ten or eleven (in M-theory)[1] spacetime dimensions, as opposed to the usual four (three spatial and one temporal) used in relativity theory; however, the theory can describe universes with four effective (observable) spacetime dimensions by a variety of methods.[2] The theories also appear to describe higher-dimensional objects than strings, called branes. Certain types of string theory have also been shown to be equivalent to certain types of more traditional gauge theory, and it is hoped that research in this direction will lead to new insights on quantum chromodynamics, the fundamental theory of the strong nuclear force.[3][4][5][6]


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

For more details on why it is hard to unite gravity and quantum physics, and on alternatives to string theory, see quantum gravity.

The idea behind all string theories is that the constituents of reality are strings of extremely small size (possibly of the order of the Planck length, about 10−35 m) which vibrate at specific resonant frequencies.[7] Thus, any particle should be thought of as a tiny vibrating object, rather than as a point. This object can vibrate in different modes (just as a guitar string can produce different notes), with every mode appearing as a different particle (electron, photon, etc.). Strings can split and combine, which would appear as particles emitting and absorbing other particles, presumably giving rise to the known interactions between particles.

In addition to strings, this theory also includes 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. String theory is thought to include some 10, 11, or 26 dimensions, depending on the specific theory and on the point of view.

Interest in string theory is driven largely by the hope that it will prove to be a consistent theory of quantum gravity or even a theory of everything. 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 the theory allows to choose those details.

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; 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).

String theory is thought to be a certain limit of another, more fundamental theory — M-theory — which is only partly defined and is not well understood.[8]

Levels of magnification: Macroscopic level, molecular level, atomic level, subatomic level, string level.

Basic properties

String theory is formulated in terms of an action principle, either the Nambu-Goto action or the Polyakov action, which describes how strings move through space and time. Like springs with no external force applied, the strings tend to shrink, thus minimizing 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 — the string can vibrate in many different modes, just like a guitar string can produce different notes. The different modes, each corresponding to a different kind of particle, make up the "spectrum" of the theory.

Strings can split and combine, which would appear as particles emitting and absorbing other particles, presumably giving rise to the known interactions between particles.

String theory includes 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 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, which incorporated only bosons, describes — in low enough energies — a quantum gravity theory, which also includes (if open strings are incorporated as well) gauge fields 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 space-time 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 fermions 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 theories; several different kinds have been described, but all are now thought to be different limits of M-theory.

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.


For more details on this topic, see 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 closed string looks like a small loop, so its worldsheet will look like a pipe, or — more generally — as a Riemannian surface (a two-dimensional 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 — as a Riemann surface 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 (often referred to as a pair of pants — 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 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 and some versions 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 non-orientable surface.


Main articles: String duality, S-duality, T-duality, and U-duality

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 one whose low energy limit, with ten spacetime dimensions compactified down to four, matched the physics observed in our world today. It is now known that this picture was naïve, 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.

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

String theories
Type Spacetime dimensions
Bosonic 26 Only bosons, no fermions, meaning 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 (achiral)
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).

Extra dimensions

Number of dimensions

One 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—more precisely different values of the "effective central charge," a count of degrees of freedom which reduces to dimensionality in weakly curved regimes—are related by dynamical transitions.[9]

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," 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 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—and the theory consistent—only for a particular number of dimensions.[10]

When the calculation is done, the critical dimensionality is not four as one may expect (three axes of space and one of time). 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.[11] Starting from any dimension greater than four, it is necessary to consider how these are reduced to four dimensional space-time.

Compact dimensions

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 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 wavelengths (of the order of the compact dimension's radius), which in quantum mechanics means very high energies (see wave-particle duality).

Brane-world scenario

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.[citation needed]

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 and Klein's early work demonstrated that general relativity with four 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


Main article: 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 boundaries are attached to them. Thus D-branes can emit and absorb closed strings; therefore they have mass (since they emit gravitons) and — in superstring theories — 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 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 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 gauge theory.

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

Gauge Bosons and D-branes

String theory states that a Gauge Boson can have each of the ends of its string on separate branes. The mass of the string (Gauge Boson) is proportional to the separation of the two branes.[12] For every Planck length that the string is stretched, approximately one Plank mass unit is gained. It was theorized by A.J.B. that the string could possibly become massive enough to become a black hole, which could be another possibility for black hole formation. For this to happen, the string would have to become compacted into a 'string ball' so that the mass could become concentrated enough to form a black hole. If such black holes were detected, they could provide evidence for string theory. They would all be roughly the same mass (which would contain information about the separation of the branes), and they would not necessarily be in galaxies. These are very interesting thoughts and they open up many possibilities.

Gauge-gravity duality

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 decoupled from the gravity living in the bulk; thus open strings attached to the D-branes are not 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-branes 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 AdS5 S5 (a product space of a five-dimensional Anti de Sitter space and a five-sphere) on one hand, and N = 4 supersymmetric Yang-Mills theory on the four-dimensional boundary of the Anti de Sitter space (either a flat four-dimensional spacetime R3,1 or a three-sphere with time S5 R).[13] 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. 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 strings, which are made of gauge bosons (gluons) and other gauge theory degrees of freedom. 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) is decreasing with the radius, then its dual field theory will be 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 nuclear force. To this end, it is hoped that a gravitational theory dual to quantum chromodynamics will be found.[14]

In fact, a vague contact with experiment has already been claimed to have be achieved[15][16][17][18] though currently the alternative, Lattice QCD, is doing a much better job and has already made contact with experiments at various fields with good results,[19] though the computations are numerical rather than analytic.

Problems and controversy

Although historically string theory is an outgrowth of physics, some contend that string theory should (strictly speaking) be classified as something other than science. For a scientific theory to be valid it must be verified empirically, i.e. through experiment or observation. Few avenues for such contact with experiment have been claimed.[20] With the construction of the Large Hadron Collider in CERN some scientists hope to produce relevant data, though it is widely believed that any theory of quantum gravity would require much higher energies to probe directly. Moreover, string theory as it is currently understood has a huge number of equally possible solutions.[21] Thus it has been claimed by some scientists that string theory may not be falsifiable and may have no predictive power.[22][23][24][25]

String theory remains to be confirmed. No version of string theory has yet made an experimentally verified prediction that differs from those made by other theories. The energy scales at which it would be possible to see the stringy nature of particles is much greater than that experimentally accessible. It possesses many features of mathematical interest and naturally incorporates all the gross features of the Standard Model, such as non-abelian gauge groups and chiral fermions. Because string theory may not be tested in the foreseeable future, some scientists[26] have asked if it even deserves to be called a scientific theory; it is not falsifiable in the sense of Popper.

It has also been suggested that string theory is better thought of as a framework for building models, in the same way that quantum field theory is a framework.[27]

Ideas from string theory have had a major influence on proposals for physics beyond the Standard Model. For example, while supersymmetry is 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. However, 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, when observing stars during a solar eclipse, the sun's gravity had not deflected light by the predicted amount, then Einstein's general relativity theory would have been proven wrong.

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.

Yet another central problem of string theory is that the best understood backgrounds of string theory preserve much of the supersymmetry of the underlying theory, which results in time-invariant space-times: currently string theory cannot deal well with time-dependent, cosmological backgrounds.

The previous two issues are related to a more profound problem: string theory might not be truly fundamental in its present formulation because it is background-dependent — string theory describes perturbative expansions about fixed spacetime backgrounds. Some see background independence as a fundamental requirement of a theory of quantum gravity, particularly since General Relativity is already background independent. In response to this criticism, some string theorists disagree that background-independence should be a guiding principle[citation needed], while others hope that M-theory, or a non-perturbative treatment of string theory (such as string field theory) will turn out to be background-independent, giving as solutions the many different versions of string theory with the different backgrounds.

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 a large number of distinct, meta-stable vacua, perhaps 10500 or more. Each of these corresponds to a different universe, with a different collection of particles and forces.[21] What principle, if any, can be used to select among these vacua is an open issue. 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 values of physical constants, in particular the small value of the cosmological constant.[28][29] However, such explanations are not usually regarded as scientific in the Popperian sense.

String theory does predict, at least perturbatively, that at sufficiently high energies—which are probably near the quantum gravity scale—the string-like nature of particles should be apparent. For example, there should be heavier copies of all particles corresponding to higher string harmonics. However, it is unclear what these energies are. In the limiting case, these energies would be one million billion (ten followed by fourteen zeros) times higher than those accessible in the newest accelerator, the LHC.

Following the appearance of two books claiming string theory is a failure,[22][25] a hot media debate is evolving as of 2007.[30][31]

"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." [2]


Main article: History of string theory

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 (see Kaluza–Klein theory). These predictions would set the foundation for string theory by introducing the concept of extra dimensions.

String theory was originally developed and explored during the late 1960s and early 1970s to explain some peculiarities of the behavior of hadrons (subatomic particles such as the proton and neutron which experience the strong nuclear force). In particular, Yoichiro Nambu (and later Lenny Susskind and Holger Nielsen) realized in 1970 that the dual resonance model of strong interactions could be explained by a quantum-mechanical model of strings. This approach was abandoned as an alternative theory, quantum chromodynamics, gained experimental support, but has recently reemerged in the context of the AdS/CFT correspondence.

During the mid-1970s it was discovered that the same mathematical formalism can be used to describe a theory of quantum gravity. This led to the development of bosonic string theory, which is still the version first taught to many students.

Between 1984 and 1986, physicists realized that string theory could describe all elementary particles and the interactions between them, and hundreds of them started to work on string theory as the most promising idea to unify theories of physics. This is known as the first 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 up many possibilities for constructing realistic cosmological models in the theory.

In 1995, at the annual conference of string theorists at the University of Southern California (USC), Edward Witten gave his famous speech on string theory that essentially united the five string theories that existed at the time, and giving birth to a new 11-dimensional theory called M-theory. This sparked the second superstring revolution.

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. Through this relationship, string theory may be related in the future to quantum chromodynamics and lead, eventually, to a better understanding of the behavior of hadrons, thus returning to its original goal.

Recently, the discovery of the string theory landscape, which suggests that string theory has an exponentially large number of different vacua, led to discussions of what string theory might eventually be expected to predict, and to the worry that the answer might continue to be nothing.

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, as well as in Australia on SBS.

* String Theory is also a trilogy of novels based on the Star Trek: Voyager television series.

* The Calabi-Yau space is mentioned in reference to a hypothetical matter quantum teleportation (QT for short) in the novels Ilium and Olympos, by Science Fiction writer Dan Simmons. In addition, several other hypothetical quantum-mechanics and string theory-related concepts are employed and to some extent explained or described in the books: Brane holes, parallel universes, singularities (black holes and wormholes), "quantum" morphing/shapeshifting devices and the intrinsic probabilistic nature of the quantum mechanical theory.

* In "H. P. Lovecraft's Dreams in the Witch-House", an episode of the Showtime series Masters of Horror (based on a story by H. P. Lovecraft and directed by Stuart Gordon), a young grad student from Miskatonic University studies interdimensional string theory in his run-down apartment and discovers the intersection of two separate realities.

* The television show Heroes episode "Five Years Gone" used to be known as "String Theory".

* The television show Sliders is based on a device capable of opening vortices to alternate dimensions.

* The song 'Supertheory Of Supereverything' by the band Gogol Bordello mentions string theory.

* Christian teacher Rob Bell puts forth his ideas of string theory in his popular teaching, Everything is Spiritual.

* String Theory featured in a recent episode of the BBC Radio 4 spoof comedy series Down the Line

* In the 24th Episode of the Action Comedy series Loonatics Unleashed called "The Music Villain" Tech Cyote explains that Rupes Oberon wants a cosmic guitar to control Zadavia's powers and mentioning the concept of the string theory.

* The popular webcomic "xkcd" referenced string theory in the comic of the same name by parodying the theory's apparent inability to explain itself. The comic "summarizes" the theory through a simple dialog: "I just had an awesome idea. Suppose all matter and energy is made of tiny, vibrating 'strings.'" "Okay. What would that imply?" "I dunno." Comic

See also

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

String theory and M-theory: a modern introduction , Katrin Becker, Melanie Becker, John H. Schwarz


1. ^ M. J. Duff, James T. Liu and R. Minasian Eleven Dimensional Origin of String/String Duality: A One Loop Test Center for Theoretical Physics, Department of Physics, Texas A&M University
2. ^ Polchinski, Joseph (1998). String Theory, Cambridge University Press.
3. ^ H. Nastase The RHIC fireball as a dual black hole BROWN-HET-1439, ArXiv: hep-th/0501068, January 2005,
4. ^ H. Nastase More on the RHIC fireball and dual black holes BROWN-HET-1466, ArXiv: hep-th/0603176, March 2006,
5. ^ H. Liu, K. Rajagopal, U. A. Wiedemann An AdS/CFT Calculation of Screening in a Hot Wind, MIT-CTP-3757, July 2006,
6. ^ H. Liu, K. Rajagopal, U. A. Wiedemann Calculating the Jet Quenching Parameter from AdS/CFT, Phys.Rev.Lett.97:182301,2006

7. ^ To compare, the size of an atom is roughly 10-10 m and the size of a proton is 10-15 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 of a string (8.9×1042 newtons) is about 1041 times the tension of an average piano string (735 newtons).

8. ^ This is most vividly captured by T-duality, a result that demonstrates that it is impossible to tell the difference between dimensions smaller than the string length and those much larger: Physical processes in a dimension of size R in one theory match those in a dimension of size 1/R of a different theory.

9. ^ Simeon Hellerman, Ian Swanson: "Dimension-changing exact solutions of string theory". e-Print: hep-th/0612051; Ofer Aharony, Eva Silverstein: "Supercritical stability, transitions and (pseudo)tachyons". Physical Review D 75:046003, 2007. e-Print: hep-th/0612031

10. ^ 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.

11. ^ "Quantum Geometry of Bosonic Strings – Revisited"

12. ^ "Warped Passages" by Lisa Randall

13. ^ Aharony, O.; S.S. Gubser, J. Maldacena, H. Ooguri, Y. Oz (2000). "Large N Field Theories, String Theory and Gravity". Phys. Rept. 323: 183-386.​. For other examples see: [1]

14. ^ 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

15. ^ H. Nastase The RHIC fireball as a dual black hole BROWN-HET-1439, ArXiv: hep-th/0501068, January 2005,

16. ^ H. Nastase More on the RHIC fireball and dual black holes BROWN-HET-1466, ArXiv: hep-th/0603176, March 2006,

17. ^ H. Liu, K. Rajagopal, U. A. Wiedemann An AdS/CFT Calculation of Screening in a Hot Wind, MIT-CTP-3757, July 2006,

18. ^ H. Liu, K. Rajagopal, U. A. Wiedemann Calculating the Jet Quenching Parameter from AdS/CFT, Phys.Rev.Lett.97:182301,2006

19. ^ See for example Recent Results of the MILC research program, taken from the MILC Collaboration homepage

20. ^ M. R. Douglas,Are There Testable Predictions of String Theory? February 2007 Texas A&M

21. ^ a b S. Kachru, R. Kallosh, A. Linde and S. P. Trivedi, de Sitter Vacua in String Theory, Phys.Rev.D68:046005,2003

22. ^ a b Peter Woit's Not Even Wrong weblog

23. ^ P. Woit (Columbia University) String theory: An Evaluation,February 2001, e-Print: physics/0102051

24. ^ P. Woit, Is String Theory Testable? INFN Rome March 2007

25. ^ a b Lee Smolin's The Trouble With Physics webpage

26. ^ Prominent critics include Philip Anderson ("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), Sheldon Glashow ("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", NOVA interview), Lawrence Krauss ("String theory [is] yet to have any real successes in explaining or predicting anything measurable", New York Times, 8 November 2005), Peter Woit (see his blog, article and book "Not Even Wrong", ISBN 0-224-07605-1) and Carlo Rovelli (see his Dialog on Quantum Gravity)

27. ^ David Gross, Perspectives, String Theory: Achievements and Perspectives - A conference

28. ^ N. Arkani-Hamed, S. Dimopoulos and S. Kachru, Predictive Landscapes and New Physics at a TeV, SLAC-PUB-10928, HUTP-05-A0001, SU-ITP-04-44, January 2005

29. ^ L. Susskind The Anthropic Landscape of String Theory, February 2003

30. ^ John Baez and responses on the group weblog The n-Category Cafe

31. ^ John Baez weblog

Further reading

Popular books and articles

* Davies, Paul; Julian R. Brown (Eds.) (July 31 1992). Superstrings: A Theory of Everything?, Reprint edition, Cambridge: Cambridge University Press, 244. ISBN 0-521-43775-X.

* Gefter, Amanda (December 2005). Is string theory in trouble?. New Scientist. Retrieved on 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 multiple universes.

* Green, Michael (September 1986). Superstrings. Scientific American. Retrieved on December 19, 2005.

* Greene, Brian (October 20 2003). The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory, Reissue edition, New York: W.W. Norton & Company, 464. ISBN 0-393-05858-1.

* Greene, Brian (2004). The Fabric of the Cosmos: Space, Time, and the Texture of Reality. New York: Alfred A. Knopf, 569. ISBN 0-375-41288-3.

* Gribbin, John (1998). The Search for Superstrings, Symmetry, and the Theory of Everything. London: Little Brown and Company, 224. ISBN 0-316-32975-4.

* Halpern, Paul (2004). The Great Beyond: Higher Dimensions, Parallel Universes, and the Extraordinary Search for a Theory of Everything. Hoboken, New Jersey: John Wiley & Sons, Inc., 326. ISBN 0-471-46595-X.

* Hooper, Dan (2006). Dark Cosmos: In Search of Our Universe's Missing Mass and Energy. New York: HarperCollins, 240. ISBN 978-0-06-113032-8.

* Kaku, Michio (April 1994). Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension. Oxford: Oxford University Press, 384. ISBN 0-19-508514-0.

* Penrose, Roger (February 22 2005). The Road to Reality: A Complete Guide to the Laws of the Universe. Knopf, 1136. ISBN 0-679-45443-8.

* Randall, Lisa (September 1 2005). Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions. New York: Ecco Press, 512. ISBN 0-06-053108-8.

* Smolin, Lee (2006). The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next. New York: Houghton Mifflin Co., 392. ISBN 0-618-55105-0.

* 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.)

* Vilenkin, Alex (2006). Many Worlds in One: The Search for Other Universes. New York: Hill and Wang, 235. ISBN 0-8090-9523-8.

* Witten, Edward (June 2002). The Universe on a String. Astronomy Magazine. Retrieved on December 19, 2005. – An easy article for everybody outside physics wanting to understand the very basics of the theory.

* Woit, Peter (2006). Not Even Wrong - The Failure of String Theory And the Search for Unity in Physical Law. London: Jonathan Cape &: New York: Basic Books, 290. ISBN 0-224-07605-1 & ISBN 978-0-465-09275-8.


* 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.
* Paul H. Frampton (1974). Dual Resonance Models. Frontiers in Physics. ISBN 0-805-32581-6.
* Gasperini, Maurizio (2007). Elements of String Cosmology, Cambridge University Press. ISBN 978-0-521-86875-4.
* Michael Green, John H. Schwarz and Edward Witten (1987). Superstring theory, Cambridge University Press. The original textbook.
o Vol. 1: Introduction. ISBN 0-521-35752-7.
o 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.
* Polchinski, Joseph (1998). String Theory, Cambridge University Press. A modern textbook.

o Vol. 1: An introduction to the bosonic string. ISBN 0-521-63303-6.
o Vol. 2: Superstring theory and beyond. ISBN 0-521-63304-4.

* Johnson, Clifford (2003). D-branes. Cambridge: Cambridge University Press. ISBN 0-521-80912-6.
* Zwiebach, Barton (2004). A First Course in String Theory, Cambridge University Press. ISBN 0-521-83143-1. Errata are available

* Katrin Becker, Melanie Becker and John H. Schwarz (2007). String Theory and M-Theory: A Modern Introduction , Cambridge University Press. ISBN 0-521-86069-5
* Leonard Susskind, (2006). The Cosmic Landscape: String Theory And The Illusion Of Intelligent Design, Little, Brown & Company ISBN 0-316-15579-9
* Szabo, Richard J. (Reprinted 2007). An Introduction to String Theory and D-brane Dynamics, Imperial College Press. ISBN 978-1-86094-427-7.


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