eng
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
Living Reviews in Relativity
1433-8351
2012-10-22
15
11
10.12942/lrr-2012-11
lrr-2012-11
article
The Kerr/CFT Correspondence and its Extensions
Geoffrey Compère
1
Physique Théorique et Mathématique, Université Libre de Bruxelles, CP 231, 1050 Bruxelles, Belgium
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.
http://www.livingreviews.org/lrr-2012-11
holography
AdS/CFT
conformal field theory
Black holes