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.
Highlights
It is known since the work of Bardeen, Bekenstein, Carter and Hawking [42, 32, 162] that black holes are thermodynamical systems equipped with a temperature and an entropy
Since quantum gravity in asymptotically AdS3 geometries is described by a two-dimensional conformal field theory (2d CFT) [58, 251], one can account for the entropy and the Hawking radiation of these supersymmetric or nearly supersymmetric black holes using only the universal properties of a dual CFT description defined in the near-horizon region [209, 104]
We show that the near-horizon regions of extremal black holes are isolated geometries, isolated thermodynamical systems and, more generally, isolated dynamical systems
Summary
It is known since the work of Bardeen, Bekenstein, Carter and Hawking [42, 32, 162] that black holes are thermodynamical systems equipped with a temperature and an entropy. Since quantum gravity in asymptotically AdS3 geometries is described by a two-dimensional conformal field theory (2d CFT) [58, 251], one can account for the entropy and the Hawking radiation of these supersymmetric or nearly supersymmetric black holes using only the universal properties of a dual CFT description defined in the near-horizon region [209, 104] (for reviews, see [155, 113]) Ultraviolet completions of these AdS/CFT correspondences can be constructed using string theory [205, 265]. We refer the interested reader to the complementary string theory-oriented review of extremal black holes [244].2
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