Anti–de Sitter–CFT correspondence in three-dimensional supergravity

Bañados, Máximo; Bautier, Karin; Coussaert, Olivier; Henneaux, Marc; Ortiz, Miguel

doi:10.1103/physrevd.58.085020

Cited by 77 publications

(118 citation statements)

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“…Instead, Eddington-Finkelstein coordinates for the metric, which cover both the conformal boundary and the static observer, lead to a highest weight gauge for both Chern-Simons gauge fields. This distinction leads to some new features of the Hamiltonian reduction to Liouville theory with respect to previous treatments [2,5,23,24]. Usually, one performs a Gauss decomposition of an SL(2, C) element around the identity in order to reduce the non-chiral WZW model to Liouville theory.…”

Section: Jhep03(2015)158mentioning

confidence: 99%

Liouville theory beyond the cosmological horizon

Compère

Donnay

Lambert

et al. 2015

J. High Energ. Phys.

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Abstract:The dS/CFT correspondence postulates the existence of a Euclidean CFT dual to a suitable gravity theory with Dirichlet boundary conditions asymptotic to de Sitter spacetime. A semi-classical model of such a correspondence consists of Einstein gravity with positive cosmological constant and without matter which is dual to Euclidean Liouville theory defined at the future conformal boundary. Here we show that Euclidean Liouville theory is also dual to Einstein gravity with Dirichlet boundary conditions on a fixed timelike slice in the static patch. Intriguingly, the spacetime interpretation of Euclidean Liouville time is the physical time of the static observer. As a prerequisite of this correspondence, we show that the asymptotic symmetry algebra which consists of two copies of the Virasoro algebra extends everywhere into the bulk.

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Section: Jhep03(2015)158mentioning

confidence: 99%

Liouville theory beyond the cosmological horizon

Compère

Donnay

Lambert

et al. 2015

J. High Energ. Phys.

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“…These boundary conditions correspond to fixed total charge or fixed electric flux (3.9). 12 The level of the U(1) current algebra can be deduced from (4.7) and the assumption that the AdS 3 central charge is c = 6k while the AdS 2 central charge is c = 0. One finds…”

Section: Jhep01(1999)008mentioning

confidence: 99%

“…We choose the normalization constants C n so that 12) with respect to the Klein-Gordon inner product…”

Section: Jhep01(1999)008mentioning

confidence: 99%

“…Perhaps the best understood of the family of AdS/CFT dualities [1] is the case AdS 3 /2D-CFT [2,1,3,4,5,6,7,8,9,10,11,12], largely because the conformal group is infinite dimensional and greatly constrains the dynamics. In higher dimensions the field theory side is less well understood, and the duality has largely been used to learn about field theory from gravity.…”

Section: Introductionmentioning

confidence: 99%

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AdS₂ quantum gravity and string theory

Strominger

1999

J. High Energy Phys.

319

506

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“…We follow [41]. (See [36] for an alternative derivation based on a twisted Sugawara construction, and [46] for a supersymmetric generalization. )…”

Section: The Brown-henneaux Conformal Symmetrymentioning

confidence: 99%

Notes on black holes and three dimensional gravity

Bañados¹

1999

AIP Conference Proceedings

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Abstract.These notes are the written version of two lectures delivered at the VIII Mexican School on Particles and Fields on November 1998. The level of the notes is basic assuming only some knowledge on Statistical Mechanics, General Relativity and YangMills theory. After a brief introduction to the classical and semiclassical aspects of black holes, we review some relevant results on 2+1 quantum gravity. These include the Chern-Simons formulation and its affine Kac-Moody algebra, the asymptotic algebra of Brown and Henneaux, and the statistical mechanics description of 2+1 black holes. Hopefully, this contribution will be complementary with the review paper hepth/9901148 by the same author, and perhaps, a shortcut to some recent developments in three dimensional gravity. I INTRODUCTIONDuring the last three years we have witnessed a rapid progress in the string theory description of general relativity. Successfull computations of black hole entropy for extremal and near extremal solutions [1,2] have made it clear that the string theory degrees of freedom describes the expected semiclassical behaviour of general relativity. This is in sharp constrast with the more standard approach to quantum gravity either based on the path integral approach or the Wheeler-de Witt equation which has provided little information about the fundamental degrees of freedom giving rise to the Bekenstein-Hawking entropy. In the Loop representation approach to quantum gravity, a computation of the black hole entropy has been proposed [3,4]. However, in this formulation it is still obscure how to introduce dynamics, and only the kinematics of spin networks is under control.In this contribution we shall consider neither string theory nor loop quantum gravity. Instead, we work in the very simple setting of three-dimensional quantum gravity whose Lagrangian describes a well-defined quantum field theory [5,6]. As motivations to study three-dimensional gravity, let us mention the following aspects of it. (i) It is a mathematically simple theory which combines three important branches of physics: General Relativity, Yang-Mills theory (with a Chern-Simons

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Anti–de Sitter–CFT correspondence in three-dimensional supergravity

Cited by 77 publications

References 50 publications

Liouville theory beyond the cosmological horizon

Liouville theory beyond the cosmological horizon

AdS₂ quantum gravity and string theory

Notes on black holes and three dimensional gravity

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Anti–de Sitter–CFT correspondence in three-dimensional supergravity

Cited by 77 publications

References 50 publications

Liouville theory beyond the cosmological horizon

Liouville theory beyond the cosmological horizon

AdS2 quantum gravity and string theory

Notes on black holes and three dimensional gravity

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AdS₂ quantum gravity and string theory