In theoretical physics, the anti-de Sitter/conformal
field theory correspondence, sometimes called
Maldacena duality or gauge/gravity duality,
is a conjectured relationship between two
kinds of physical theories. On one side are
anti-de Sitter spaces (AdS) which are used
in theories of quantum gravity, formulated
in terms of string theory or M-theory. On
the other side of the correspondence are conformal
field theories (CFT) which are quantum field
theories, including theories similar to the
Yang–Mills theories that describe elementary
particles.
The duality represents a major advance in
our understanding of string theory and quantum
gravity. This is because it provides a non-perturbative
formulation of string theory with certain
boundary conditions and because it is the
most successful realization of the holographic
principle, an idea in quantum gravity originally
proposed by Gerard 't Hooft and promoted by
Leonard Susskind.
It also provides a powerful toolkit for studying
strongly coupled quantum field theories. Much
of the usefulness of the duality results from
the fact that it is a strong-weak duality:
when the fields of the quantum field theory
are strongly interacting, the ones in the
gravitational theory are weakly interacting
and thus more mathematically tractable. This
fact has been used to study many aspects of
nuclear and condensed matter physics by translating
problems in those subjects into more mathematically
tractable problems in string theory.
The AdS/CFT correspondence was first proposed
by Juan Maldacena in late 1997. Important
aspects of the correspondence were elaborated
in articles by Steven Gubser, Igor Klebanov,
and Alexander Polyakov, and by Edward Witten.
By 2015, Maldacena's article had over 10,000
citations, becoming the most highly cited
article in the field of high energy physics.
== Background ==
=== 
Quantum gravity and strings ===
Current understanding of gravity is based
on Albert Einstein's general theory of relativity.
Formulated in 1915, general relativity explains
gravity in terms of the geometry of space
and time, or spacetime. It is formulated in
the language of classical physics developed
by physicists such as Isaac Newton and James
Clerk Maxwell. The other nongravitational
forces are explained in the framework of quantum
mechanics. Developed in the first half of
the twentieth century by a number of different
physicists, quantum mechanics provides a radically
different way of describing physical phenomena
based on probability.Quantum gravity is the
branch of physics that seeks to describe gravity
using the principles of quantum mechanics.
Currently, the most popular approach to quantum
gravity is string theory, which models elementary
particles not as zero-dimensional points but
as one-dimensional objects called strings.
In the AdS/CFT correspondence, one typically
considers theories of quantum gravity derived
from string theory or its modern extension,
M-theory.In everyday life, there are three
familiar dimensions of space (up/down, left/right,
and forward/backward), and there is one dimension
of time. Thus, in the language of modern physics,
one says that spacetime is four-dimensional.
One peculiar feature of string theory and
M-theory is that these theories require extra
dimensions of spacetime for their mathematical
consistency: in string theory spacetime is
ten-dimensional, while in M-theory it is eleven-dimensional.
The quantum gravity theories appearing in
the AdS/CFT correspondence are typically obtained
from string and M-theory by a process known
as compactification. This produces a theory
in which spacetime has effectively a lower
number of dimensions and the extra dimensions
are "curled up" into circles.A standard analogy
for compactification is to consider a multidimensional
object such as a garden hose. If the hose
is viewed from a sufficient distance, it appears
to have only one dimension, its length, but
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.
=== Quantum field theory ===
The application of quantum mechanics to physical
objects such as the electromagnetic field,
which are extended in space and time, is known
as quantum field theory. In particle physics,
quantum field theories form the basis for
our understanding of elementary particles,
which are modeled as excitations in the fundamental
fields. Quantum field theories are also used
throughout condensed matter physics to model
particle-like objects called quasiparticles.In
the AdS/CFT correspondence, one considers,
in addition to a theory of quantum gravity,
a certain kind of quantum field theory called
a conformal field theory. This is a particularly
symmetric and mathematically well behaved
type of quantum field theory. Such theories
are often studied in the context of string
theory, where they are associated with the
surface swept out by a string propagating
through spacetime, and in statistical mechanics,
where they model systems at a thermodynamic
critical point.
== Overview of the correspondence ==
=== 
The geometry of anti-de Sitter space ===
In the AdS/CFT correspondence, one considers
string theory or M-theory on an anti-de Sitter
background. This means that the geometry of
spacetime is described in terms of a certain
vacuum solution of Einstein's equation called
anti-de Sitter space.In very elementary terms,
anti-de Sitter space is a mathematical model
of spacetime in which the notion of distance
between points (the metric) is different from
the notion of distance in ordinary Euclidean
geometry. It is closely related to hyperbolic
space, which can be viewed as a disk as illustrated
on the right. This image shows a tessellation
of a disk by triangles and squares. One can
define the distance between points of this
disk in such a way that all the triangles
and squares are the same size and the circular
outer boundary is infinitely far from any
point in the interior.Now imagine a stack
of hyperbolic disks where each disk represents
the state of the universe at a given time.
The resulting geometric object is three-dimensional
anti-de Sitter space. It looks like a solid
cylinder in which any cross section is a copy
of the hyperbolic disk. Time runs along the
vertical direction in this picture. The surface
of this cylinder plays an important role in
the AdS/CFT correspondence. As with the hyperbolic
plane, anti-de Sitter space is curved in such
a way that any point in the interior is actually
infinitely far from this boundary surface.
This construction describes a hypothetical
universe with only two space and one time
dimension, but it can be generalized to any
number of dimensions. Indeed, hyperbolic space
can have more than two dimensions and one
can "stack up" copies of hyperbolic space
to get higher-dimensional models of anti-de
Sitter space.
=== The idea of AdS/CFT ===
An important feature of anti-de Sitter space
is its boundary (which looks like a cylinder
in the case of three-dimensional anti-de Sitter
space). One property of this boundary is that,
locally around any point, it looks just like
Minkowski space, the model of spacetime used
in nongravitational physics.One can therefore
consider an auxiliary theory in which "spacetime"
is given by the boundary of anti-de Sitter
space. This observation is the starting point
for AdS/CFT correspondence, which states that
the boundary of anti-de Sitter space can be
regarded as the "spacetime" for a conformal
field theory. The claim is that this conformal
field theory is equivalent to the gravitational
theory on the bulk anti-de Sitter space in
the sense that there is a "dictionary" for
translating calculations in one theory into
calculations in the other. Every entity in
one theory has a counterpart in the other
theory. For example, a single particle in
the gravitational theory might correspond
to some collection of particles in the boundary
theory. In addition, the predictions in the
two theories are quantitatively identical
so that if two particles have a 40 percent
chance of colliding in the gravitational theory,
then the corresponding collections in the
boundary theory would also have a 40 percent
chance of colliding.
Notice that the boundary of anti-de Sitter
space has fewer dimensions than anti-de Sitter
space itself. For instance, in the three-dimensional
example illustrated above, the boundary is
a two-dimensional surface. The AdS/CFT correspondence
is often described as a "holographic duality"
because this relationship between the two
theories is similar to the relationship between
a three-dimensional object and its image as
a hologram. Although a hologram is two-dimensional,
it encodes information about all three dimensions
of the object it represents. In the same way,
theories which are related by the AdS/CFT
correspondence are conjectured to be exactly
equivalent, despite living in different numbers
of dimensions. The conformal field theory
is like a hologram which captures information
about the higher-dimensional quantum gravity
theory.
=== Examples of the correspondence ===
Following Maldacena's insight in 1997, theorists
have discovered many different realizations
of the AdS/CFT correspondence. These relate
various conformal field theories to compactifications
of string theory and M-theory in various numbers
of dimensions. The theories involved are generally
not viable models of the real world, but they
have certain features, such as their particle
content or high degree of symmetry, which
make them useful for solving problems in quantum
field theory and quantum gravity.The most
famous example of the AdS/CFT correspondence
states that type IIB string theory on the
product space
A
d
S
5
×
S
5
{\displaystyle AdS_{5}\times S^{5}}
is equivalent to N = 4 supersymmetric Yang–Mills
theory on the four-dimensional boundary. In
this example, the spacetime on which the gravitational
theory lives is effectively five-dimensional
(hence the notation
A
d
S
5
{\displaystyle AdS_{5}}
), and there are five additional compact dimensions
(encoded by the
S
5
{\displaystyle S^{5}}
factor). In the real world, spacetime is four-dimensional,
at least macroscopically, so this version
of the correspondence does not provide a realistic
model of gravity. Likewise, the dual theory
is not a viable model of any real-world system
as it assumes a large amount of supersymmetry.
Nevertheless, as explained below, this boundary
theory shares some features in common with
quantum chromodynamics, the fundamental theory
of the strong force. It describes particles
similar to the gluons of quantum chromodynamics
together with certain fermions. As a result,
it has found applications in nuclear physics,
particularly in the study of the quark–gluon
plasma.Another realization of the correspondence
states that M-theory on
A
d
S
7
×
S
4
{\displaystyle AdS_{7}\times S^{4}}
is equivalent to the so-called (2,0)-theory
in six dimensions. In this example, the spacetime
of the gravitational theory is effectively
seven-dimensional. The existence of the (2,0)-theory
that appears on one side of the duality is
predicted by the classification of superconformal
field theories. It is still poorly understood
because it is a quantum mechanical theory
without a classical limit. Despite the inherent
difficulty in studying this theory, it is
considered to be an interesting object for
a variety of reasons, both physical and mathematical.Yet
another realization of the correspondence
states that M-theory on
A
d
S
4
×
S
7
{\displaystyle AdS_{4}\times S^{7}}
is equivalent to the ABJM superconformal field
theory in three dimensions. Here the gravitational
theory has four noncompact dimensions, so
this version of the correspondence provides
a somewhat more realistic description of gravity.
== Applications to quantum gravity ==
=== A non-perturbative formulation of string
theory ===
In quantum field theory, one typically computes
the probabilities of various physical events
using the techniques of perturbation theory.
Developed by Richard Feynman and others in
the first half of the twentieth century, perturbative
quantum field theory uses special diagrams
called Feynman diagrams to organize computations.
One imagines that these diagrams depict the
paths of point-like particles and their interactions.
Although this formalism is extremely useful
for making predictions, these predictions
are only possible when the strength of the
interactions, the coupling constant, is small
enough to reliably describe the theory as
being close to a theory without interactions.The
starting point for string theory is the idea
that the point-like particles of quantum field
theory can also be modeled as one-dimensional
objects called strings. The interaction of
strings is most straightforwardly defined
by generalizing the perturbation theory used
in ordinary quantum field theory. At the level
of Feynman diagrams, this means replacing
the one-dimensional diagram representing the
path of a point particle by a two-dimensional
surface representing the motion of a string.
Unlike in quantum field theory, string theory
does not yet have a full non-perturbative
definition, so many of the theoretical questions
that physicists would like to answer remain
out of reach.The problem of developing a non-perturbative
formulation of string theory was one of the
original motivations for studying the AdS/CFT
correspondence. As explained above, the correspondence
provides several examples of quantum field
theories which are equivalent to string theory
on anti-de Sitter space. One can alternatively
view this correspondence as providing a definition
of string theory in the special case where
the gravitational field is asymptotically
anti-de Sitter (that is, when the gravitational
field resembles that of anti-de Sitter space
at spatial infinity). Physically interesting
quantities in string theory are defined in
terms of quantities in the dual quantum field
theory.
=== Black hole information paradox ===
In 1975, Stephen Hawking published a calculation
which suggested that black holes are not completely
black but emit a dim radiation due to quantum
effects near the event horizon. At first,
Hawking's result posed a problem for theorists
because it suggested that black holes destroy
information. More precisely, Hawking's calculation
seemed to conflict with one of the basic postulates
of quantum mechanics, which states that physical
systems evolve in time according to the Schrödinger
equation. This property is usually referred
to as unitarity of time evolution. The apparent
contradiction between Hawking's calculation
and the unitarity postulate of quantum mechanics
came to be known as the black hole information
paradox.The AdS/CFT correspondence resolves
the black hole information paradox, at least
to some extent, because it shows how a black
hole can evolve in a manner consistent with
quantum mechanics in some contexts. Indeed,
one can consider black holes in the context
of the AdS/CFT correspondence, and any such
black hole corresponds to a configuration
of particles on the boundary of anti-de Sitter
space. These particles obey the usual rules
of quantum mechanics and in particular evolve
in a unitary fashion, so the black hole must
also evolve in a unitary fashion, respecting
the principles of quantum mechanics. In 2005,
Hawking announced that the paradox had been
settled in favor of information conservation
by the AdS/CFT correspondence, and he suggested
a concrete mechanism by which black holes
might preserve information.
== Applications to quantum field theory ==
=== 
Nuclear physics ===
One physical system which has been studied
using the AdS/CFT correspondence is the quark–gluon
plasma, an exotic state of matter produced
in particle accelerators. This state of matter
arises for brief instants when heavy ions
such as gold or lead nuclei are collided at
high energies. Such collisions cause the quarks
that make up atomic nuclei to deconfine at
temperatures of approximately two trillion
kelvins, conditions similar to those present
at around
10
−
11
{\displaystyle 10^{-11}}
seconds after the Big Bang.The physics of
the quark–gluon plasma is governed by quantum
chromodynamics, but this theory is mathematically
intractable in problems involving the quark–gluon
plasma. In an article appearing in 2005, Đàm
Thanh Sơn and his collaborators showed that
the AdS/CFT correspondence could be used to
understand some aspects of the quark–gluon
plasma by describing it in the language of
string theory. By applying the AdS/CFT correspondence,
Sơn and his collaborators were able to describe
the quark gluon plasma in terms of black holes
in five-dimensional spacetime. The calculation
showed that the ratio of two quantities associated
with the quark–gluon plasma, the shear viscosity
η
{\displaystyle \eta }
and volume density of entropy
s
{\displaystyle s}
, should be approximately equal to a certain
universal constant:
η
s
≈
ℏ
4
π
k
{\displaystyle {\frac {\eta }{s}}\approx {\frac
{\hbar }{4\pi k}}}
where
ℏ
{\displaystyle \hbar }
denotes the reduced Planck's constant and
k
{\displaystyle k}
is Boltzmann's constant. In addition, the
authors conjectured that this universal constant
provides a lower bound for
η
/
s
{\displaystyle \eta /s}
in a large class of systems. In 2008, the
predicted value of this ratio for the quark–gluon
plasma was confirmed at the Relativistic Heavy
Ion Collider at Brookhaven National Laboratory.Another
important property of the quark–gluon plasma
is that very high energy quarks moving through
the plasma are stopped or "quenched" after
traveling only a few femtometers. This phenomenon
is characterized by a number
q
^
{\displaystyle {\widehat {q}}}
called the jet quenching parameter, which
relates the energy loss of such a quark to
the squared distance traveled through the
plasma. Calculations based on the AdS/CFT
correspondence have allowed theorists to estimate
q
^
{\displaystyle {\widehat {q}}}
, and the results agree roughly with the measured
value of this parameter, suggesting that the
AdS/CFT correspondence will be useful for
developing a deeper understanding of this
phenomenon.
=== Condensed matter physics ===
Over the decades, experimental condensed matter
physicists have discovered a number of exotic
states of matter, including superconductors
and superfluids. These states are described
using the formalism of quantum field theory,
but some phenomena are difficult to explain
using standard field theoretic techniques.
Some condensed matter theorists including
Subir Sachdev hope that the AdS/CFT correspondence
will make it possible to describe these systems
in the language of string theory and learn
more about their behavior.So far some success
has been achieved in using string theory methods
to describe the transition of a superfluid
to an insulator. A superfluid is a system
of electrically neutral atoms that flows without
any friction. Such systems are often produced
in the laboratory using liquid helium, but
recently experimentalists have developed new
ways of producing artificial superfluids by
pouring trillions of cold atoms into a lattice
of criss-crossing lasers. These atoms initially
behave as a superfluid, but as experimentalists
increase the intensity of the lasers, they
become less mobile and then suddenly transition
to an insulating state. During the transition,
the atoms behave in an unusual way. For example,
the atoms slow to a halt at a rate that depends
on the temperature and on Planck's constant,
the fundamental parameter of quantum mechanics,
which does not enter into the description
of the other phases. This behavior has recently
been understood by considering a dual description
where properties of the fluid are described
in terms of a higher dimensional black hole.
=== Criticism ===
With many physicists turning towards string-based
methods to attack problems in nuclear and
condensed matter physics, some theorists working
in these areas have expressed doubts about
whether the AdS/CFT correspondence can provide
the tools needed to realistically model real-world
systems. In a talk at the Quark Matter conference
in 2006, an American physicist, Larry McLerran
pointed out that the N=4 super Yang–Mills
theory that appears in the AdS/CFT correspondence
differs significantly from quantum chromodynamics,
making it difficult to apply these methods
to nuclear physics. According to McLerran,
N
=
4
{\displaystyle N=4}
supersymmetric Yang–Mills is not QCD ... It
has no mass scale and is conformally invariant.
It has no confinement and no running coupling
constant. It is supersymmetric. It has no
chiral symmetry breaking or mass generation.
It has six scalar and fermions in the adjoint
representation ... It may be possible to correct
some or all of the above problems, or, for
various physical problems, some of the objections
may not be relevant. As yet there is not consensus
nor compelling arguments for the conjectured
fixes or phenomena which would insure that
the
N
=
4
{\displaystyle N=4}
supersymmetric Yang Mills results would reliably
reflect QCD.
In a letter to Physics Today, Nobel laureate
Philip W. Anderson voiced similar concerns
about applications of AdS/CFT to condensed
matter physics, stating
As a very general problem with the AdS/CFT
approach in condensed-matter theory, we can
point to those telltale initials "CFT"—conformal
field theory. Condensed-matter problems are,
in general, neither relativistic nor conformal.
Near a quantum critical point, both time and
space may be scaling, but even there we still
have a preferred coordinate system and, usually,
a lattice. There is some evidence of other
linear-T phases to the left of the strange
metal about which they are welcome to speculate,
but again in this case the condensed-matter
problem is overdetermined by experimental
facts.
== History and development ==
=== 
String theory and nuclear physics ===
The discovery of the AdS/CFT correspondence
in late 1997 was the culmination of a long
history of efforts to relate string theory
to nuclear physics. In fact, string theory
was originally developed during the late 1960s
and early 1970s as a theory of hadrons, the
subatomic particles like the proton and neutron
that are held together by the strong nuclear
force. The idea was that each of these particles
could be viewed as a different oscillation
mode of a string. In the late 1960s, experimentalists
had found that hadrons fall into families
called Regge trajectories with squared energy
proportional to angular momentum, and theorists
showed that this relationship emerges naturally
from the physics of a rotating relativistic
string.On the other hand, attempts to model
hadrons as strings faced serious problems.
One problem was that string theory includes
a massless spin-2 particle whereas no such
particle appears in the physics of hadrons.
Such a particle would mediate a force with
the properties of gravity. In 1974, Joel Scherk
and John Schwarz suggested that string theory
was therefore not a theory of nuclear physics
as many theorists had thought but instead
a theory of quantum gravity. At the same time,
it was realized that hadrons are actually
made of quarks, and the string theory approach
was abandoned in favor of quantum chromodynamics.In
quantum chromodynamics, quarks have a kind
of charge that comes in three varieties called
colors. In a paper from 1974, Gerard 't Hooft
studied the relationship between string theory
and nuclear physics from another point of
view by considering theories similar to quantum
chromodynamics, where the number of colors
is some arbitrary number
N
{\displaystyle N}
, rather than three. In this article, 't Hooft
considered a certain limit where
N
{\displaystyle N}
tends to infinity and argued that in this
limit certain calculations in quantum field
theory resemble calculations in string theory.
=== Black holes and holography ===
In 1975, Stephen Hawking published a calculation
which suggested that black holes are not completely
black but emit a dim radiation due to quantum
effects near the event horizon. This work
extended previous results of Jacob Bekenstein
who had suggested that black holes have a
well defined entropy. At first, Hawking's
result appeared to contradict one of the main
postulates of quantum mechanics, namely the
unitarity of time evolution. Intuitively,
the unitarity postulate says that quantum
mechanical systems do not destroy information
as they evolve from one state to another.
For this reason, the apparent contradiction
came to be known as the black hole information
paradox.
Later, in 1993, Gerard 't Hooft wrote a speculative
paper on quantum gravity in which he revisited
Hawking's work on black hole thermodynamics,
concluding that the total number of degrees
of freedom in a region of spacetime surrounding
a black hole is proportional to the surface
area of the horizon. This idea was promoted
by Leonard Susskind and is now known as the
holographic principle. The holographic principle
and its realization in string theory through
the AdS/CFT correspondence have helped elucidate
the mysteries of black holes suggested by
Hawking's work and are believed to provide
a resolution of the black hole information
paradox. In 2004, Hawking conceded that black
holes do not violate quantum mechanics, and
he suggested a concrete mechanism by which
they might preserve information.
=== Maldacena's paper ===
In late 1997, Juan Maldacena published a landmark
paper that initiated the study of AdS/CFT.
According to Alexander Markovich Polyakov,
"[Maldacena's] work opened the flood gates."
The conjecture immediately excited great interest
in the string theory community and was considered
in articles by Steven Gubser, Igor Klebanov
and Polyakov, and by Edward Witten. These
papers made Maldacena's conjecture more precise
and showed that the conformal field theory
appearing in the correspondence lives on the
boundary of anti-de Sitter space.
One special case of Maldacena's proposal says
that N=4 super Yang–Mills theory, a gauge
theory similar in some ways to quantum chromodynamics,
is equivalent to string theory in five-dimensional
anti-de Sitter space. This result helped clarify
the earlier work of 't Hooft on the relationship
between string theory and quantum chromodynamics,
taking string theory back to its roots as
a theory of nuclear physics. Maldacena's results
also provided a concrete realization of the
holographic principle with important implications
for quantum gravity and black hole physics.
By the year 2015, Maldacena's paper had become
the most highly cited paper in high energy
physics with over 10,000 citations. These
subsequent articles have provided considerable
evidence that the correspondence is correct,
although so far it has not been rigorously
proved.
=== AdS/CFT finds applications ===
In 1999, after taking a job at Columbia University,
nuclear physicist Đàm Thanh Sơn paid a
visit to Andrei Starinets, a friend from Sơn's
undergraduate days who happened to be doing
a Ph.D. in string theory at New York University.
Although the two men had no intention of collaborating,
Sơn soon realized that the AdS/CFT calculations
Starinets was doing could shed light on some
aspects of the quark–gluon plasma, an exotic
state of matter produced when heavy ions are
collided at high energies. In collaboration
with Starinets and Pavel Kovtun, Sơn was
able to use the AdS/CFT correspondence to
calculate a key parameter of the plasma. As
Sơn later recalled, "We turned the calculation
on its head to give us a prediction for the
value of the shear viscosity of a plasma ... A
friend of mine in nuclear physics joked that
ours was the first useful paper to come out
of string theory."Today physicists continue
to look for applications of the AdS/CFT correspondence
in quantum field theory. In addition to the
applications to nuclear physics advocated
by Đàm Thanh Sơn and his collaborators,
condensed matter physicists such as Subir
Sachdev have used string theory methods to
understand some aspects of condensed matter
physics. A notable result in this direction
was the description, via the AdS/CFT correspondence,
of the transition of a superfluid to an insulator.
Another emerging subject is the fluid/gravity
correspondence, which uses the AdS/CFT correspondence
to translate problems in fluid dynamics into
problems in general relativity.
== Generalizations ==
=== Three-dimensional gravity ===
In order to better understand the quantum
aspects of gravity in our four-dimensional
universe, some physicists have considered
a lower-dimensional mathematical model in
which spacetime has only two spatial dimensions
and one time dimension. In this setting, the
mathematics describing the gravitational field
simplifies drastically, and one can study
quantum gravity using familiar methods from
quantum field theory, eliminating the need
for string theory or other more radical approaches
to quantum gravity in four dimensions.Beginning
with the work of J. D. Brown and Marc Henneaux
in 1986, physicists have noticed that quantum
gravity in a three-dimensional spacetime is
closely related to two-dimensional conformal
field theory. In 1995, Henneaux and his coworkers
explored this relationship in more detail,
suggesting that three-dimensional gravity
in anti-de Sitter space is equivalent to the
conformal field theory known as Liouville
field theory. Another conjecture formulated
by Edward Witten states that three-dimensional
gravity in anti-de Sitter space is equivalent
to a conformal field theory with monster group
symmetry. These conjectures provide examples
of the AdS/CFT correspondence that do not
require the full apparatus of string or M-theory.
=== dS/CFT correspondence ===
Unlike our universe, which is now known to
be expanding at an accelerating rate, anti-de
Sitter space is neither expanding nor contracting.
Instead it looks the same at all times. In
more technical language, one says that anti-de
Sitter space corresponds to a universe with
a negative cosmological constant, whereas
the real universe has a small positive cosmological
constant.Although the properties of gravity
at short distances should be somewhat independent
of the value of the cosmological constant,
it is desirable to have a version of the AdS/CFT
correspondence for positive cosmological constant.
In 2001, Andrew Strominger introduced a version
of the duality called the dS/CFT correspondence.
This duality involves a model of spacetime
called de Sitter space with a positive cosmological
constant. Such a duality is interesting from
the point of view of cosmology since many
cosmologists believe that the very early universe
was close to being de Sitter space. Our universe
may also resemble de Sitter space in the distant
future.
=== Kerr/CFT correspondence ===
Although the AdS/CFT correspondence is often
useful for studying the properties of black
holes, most of the black holes considered
in the context of AdS/CFT are physically unrealistic.
Indeed, as explained above, most versions
of the AdS/CFT correspondence involve higher-dimensional
models of spacetime with unphysical supersymmetry.
In 2009, Monica Guica, Thomas Hartman, Wei
Song, and Andrew Strominger showed that the
ideas of AdS/CFT could nevertheless be used
to understand certain astrophysical black
holes. More precisely, their results apply
to black holes that are approximated by extremal
Kerr black holes, which have the largest possible
angular momentum compatible with a given mass.
They showed that such black holes have an
equivalent description in terms of conformal
field theory. The Kerr/CFT correspondence
was later extended to black holes with lower
angular momentum.
=== Higher spin gauge theories ===
The AdS/CFT correspondence is closely related
to another duality conjectured by Igor Klebanov
and Alexander Markovich Polyakov in 2002.
This duality states that certain "higher spin
gauge theories" on anti-de Sitter space are
equivalent to conformal field theories with
O(N) symmetry. Here the theory in the bulk
is a type of gauge theory describing particles
of arbitrarily high spin. It is similar to
string theory, where the excited modes of
vibrating strings correspond to particles
with higher spin, and it may help to better
understand the string theoretic versions of
AdS/CFT and possibly even prove the correspondence.
In 2010, Simone Giombi and Xi Yin obtained
further evidence for this duality by computing
quantities called three-point functions.
== See also ==
Algebraic holography
Ambient construction
Randall–Sundrum model
== Notes
