Vol. 15 (2012) > lrr-2012-11

doi: 10.12942/lrr-2012-11
Living Rev. Relativity 15 (2012), 11

The Kerr/CFT Correspondence and its Extensions

1 Physique Théorique et Mathématique, Université Libre de Bruxelles, CP 231, 1050 Bruxelles, Belgium

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Article Abstract

We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory, filling a few gaps in the literature when necessary. Firstly, we review properties of extremal black holes that imply, according to semi-classical quantization rules, that their near-horizon quantum states form a centrally-extended representation of the one-dimensional conformal group. This motivates the conjecture that the extremal Kerr and Reissner–Nordström black holes are dual to the chiral limit of a two-dimensional CFT. We also motivate the existence of an SL (2,ℤ) family of two-dimensional CFTs, which describe in their chiral limit the extremal Kerr–Newman black hole. We present generalizations in anti-de Sitter spacetime and discuss other matter-coupling and higher-derivative corrections. Secondly, we show how a near-chiral limit of these CFTs reproduces the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review how the hidden conformal symmetries of asymptotically-flat black holes away from extremality, combined with their properties at extremality, allow for a microscopic accounting of the entropy of non-extremal asymptotically-flat rotating or charged black holes. We conclude with a list of open problems.

Keywords: conformal field theory, Black holes, holography, AdS/CFT

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Since a Living Reviews in Relativity article may evolve over time, please cite the access <date>, which uniquely identifies the version of the article you are referring to:

Geoffrey Compère,
"The Kerr/CFT Correspondence and its Extensions",
Living Rev. Relativity 15,  (2012),  11. URL (cited on <date>):
http://www.livingreviews.org/lrr-2012-11

Article History

ORIGINAL http://www.livingreviews.org/lrr-2012-11
Title The Kerr/CFT Correspondence and its Extensions
Author Geoffrey Compère
Date accepted 13 June 2012, published 22 October 2012
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