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String theory

2007 Schools Wikipedia Selection. Related subjects: General Physics

   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
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   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. String theorists are attempting to adjust
   the Standard Model by removing the assumption in quantum mechanics that
   particles are point-like. By removing this assumption and replacing the
   point-like particles with strings, it is hoped that string theory will
   develop into a sensible quantum theory of gravity. Moreover, string
   theory appears to be able to "unify" the known natural forces
   (gravitational, electromagnetic, weak and strong) by describing them
   with the same set of equations.

   No experimental verification or falsification of the theory has yet
   been possible, thus leading many experts to turn to the alternate
   model, Loop quantum gravity. However, with the construction of the
   Large Hadron Collider near Geneva, Switzerland scientists may produce
   relevant data.

   Studies of string theory have revealed that it predicts not just
   strings, but also higher-dimensional objects ( branes). String theory
   strongly suggests the existence of ten or eleven (in M-theory)
   spacetime dimensions, as opposed to the relativistic four (three
   spatial and one time).

Overview

   The basic idea behind all string theories is that the fundamental
   constituents of reality are strings of extremely small scale (possibly
   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. 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, 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. 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 behaviour 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
   profound theory - M-theory - which is only partly defined and is not
   well understood.

   A key consequence of the theory is that there is no obvious operational
   way to probe distances shorter than the string length.

History

   String theory
     * bosonic string theory
     * superstring theory
          + type I string
          + type II string
          + heterotic string
     * M-theory ( simplified)
     * string field theory
     * strings
     * branes

   Related topics
     * quantum field theory
          + gauge theory
          + conformal field theory
          + topological field theory
     * supersymmetry
     * supergravity
     * general relativity
     * quantum gravity

   See also
     * string theory topics

   String theory was originally invented and explored during the late
   1960s and early 1970s, to explain some peculiarities of the behaviour
   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.

   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 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.
   Through this relationship, string theory may be related in the future
   to quantum chromodynamics and lead, eventually, to a better
   understanding of the behaviour 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.

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, 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 — 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 Yang-Mills 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 behaviour. 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 one theory (the 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.

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 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 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 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 non-orientable surface.

Dualities

   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
   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 E[8]×E[8]

   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 E[8]×E[8]). 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 behaviour
   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

   Suppose we are in ten spacetime dimensions, which means we have nine
   space dimensions 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
   stretched against its tension, so it contributes an amount of energy of
   the form wR/L_{st}^2 , where L[st] is a constant called 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
   (one with a large radius and the other with a small radius) 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 centre (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.

S-duality

   Every force has a coupling constant, which is a measure of its
   strength, and determines the chances of one particle to emit or absorb
   another particle. For electromagnetism, the coupling constant is
   proportional to the square of the electric charge. When physicists
   study the quantum behaviour of electromagnetism, they can't solve the
   whole theory exactly, because every particle may emit and absorb many
   other particles, which may also do the same, endlessly. So events of
   emission and absorption 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.

   Furthermore, type IIA theory in strong coupling behaves like an
   11-dimensional theory, with the dilaton field playing the role of an
   eleventh dimension. This 11-dimensional theory is known as M-theory.

   Unlike the T-duality, however, S-duality has not been proven to even a
   physics level of rigor for any of the aforementioned cases. It remains,
   strictly speaking, a conjecture, although most string theorists believe
   in its validity.

Extra dimensions

   One intriguing feature of string theory is that it predicts the
   possible number of dimensions in the universe. 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 (see Kaluza–Klein theory).

   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.

   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 G[2] 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 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.

D-branes

   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.

   Thus D-branes are 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-gravity 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.

   The most known example and the first one to be studied is the duality
   between Type IIB supergravity on AdS^5 * S^5 (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 R^3,1 or a three-sphere with time S^3* R). 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 has 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.
   Unsolved problems 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?

Problems and controversy

   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. In this sense, string theory is still in a
   "larval stage": it is not a proper physical theory. It possesses many
   features of mathematical interest and may yet become important in our
   understanding of the universe, but it requires further developments
   before it is accepted or discarded. 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 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 by the predicted
   amount, 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.

   Philosophically, string theory cannot be truly fundamental in its
   present formulation because it is background-dependent: each string
   theory is built on a fixed spacetime background. Since a dynamic
   spacetime is the central tenet of general relativity, the hope is that
   M-theory will turn out to be background-independent, giving as
   solutions the many different versions of string theories, but no one
   yet knows how such a fundamental theory can be constructed. A related
   problem is that the best understood backgrounds of string theory
   preserve much of the supersymmetry of the underlying theory, and thus
   are time-invariant: string theory cannot yet deal well with
   time-dependent, cosmological 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
   vacua, perhaps 10^500 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 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. However, such explanations are not usually regarded as
   scientific in the Popperian sense.

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 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".
     * Another 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, and is not related to accepted String
       Theory. 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, as the main character of the show does.
     * Both the String Theory and the Calabi-Yau Model are mentioned in
       reference to teleportation in the popular video game Half-Life 2.
     * In an episode of Criminal Minds, a Schizophrenic hostage taker
       named Ted Bryar had completed a PhD in string theory in the '80s.
     * In an episode of Masters of Horror directed by Stuart Gordon, a
       young grad student from Miskatonic University studies
       interdimensional string theory in his run-down apartment. Based on
       the short story "Dreams in the Witch-House" by H.P. Lovecraft.
     * On the popular CBS drama, Numb3rs, one of the supporting
       characters, physicist professor Dr. Larry Fleinhardt ( Peter
       MacNicol), actively researches string theory at 'Cal-Sci' (based on
       Caltech).

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