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AdS/CFT correspondence
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== Generalizations == === Three-dimensional gravity === {{Main|(2+1)-dimensional topological 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.{{refn|For a review, see {{harvnb|Carlip|2003}}.}} 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.{{refn|According to the results of {{harvnb|Witten|1988}}, three-dimensional quantum gravity can be understood by relating it to [[Chern–Simons theory]].}} Beginning with the work of J. David Brown and [[Marc Henneaux]] in 1986,{{sfn|ps=|Brown|Henneaux|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]].{{sfn|ps=|Coussaert|Henneaux|van Driel|1995}} 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.{{sfn|ps=|Witten|2007}} These conjectures provide examples of the AdS/CFT correspondence that do not require the full apparatus of string or M-theory.{{sfn|ps=|Guica|Hartman|Song|Strominger|2009|p=1}} === dS/CFT correspondence === {{Main|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.{{sfn|Maldacena|2005|p=60}} 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.{{sfn|ps=|Perlmutter|2003}} Although the properties of gravity at short distances should be somewhat independent of the value of the cosmological constant,{{sfn|ps=|Biquard|2005|p=33}} 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]].{{sfn|ps=|Strominger|2001}} 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.{{sfn|Maldacena|2005|p=60}} === Kerr/CFT correspondence === {{Main|Kerr/CFT correspondence}} Although the AdS/CFT correspondence is often useful for studying the properties of black holes,{{refn|See subsection ''{{slink|#Black hole information paradox}}''.}} 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 black hole|extremal]] [[Kerr black hole]]s, which have the largest possible angular momentum compatible with a given mass.{{sfn|ps=|Guica|Hartman|Song|Strominger|2009}} 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.{{sfn|ps=|Castro|Maloney|Strominger|2010}} === Higher spin gauge theories === The AdS/CFT correspondence is closely related to another duality conjectured by Igor Klebanov and Alexander Markovich Polyakov in 2002.{{sfn|ps=|Klebanov|Polyakov|2002}} This duality states that certain "higher spin gauge theories" on anti-de Sitter space are equivalent to conformal field theories with [[orthogonal group|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 [[mathematical proof|prove]] the correspondence.{{refn|See the Introduction in {{harvnb|Klebanov|Polyakov|2002}}.}} In 2010, Simone Giombi and Xi Yin obtained further evidence for this duality by computing quantities called [[correlation function (quantum field theory)|three-point functions]].{{sfn|ps=|Giombi|Yin|2010}}
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