Extremal black hole/CFT correspondence in (gauged) supergravities

Abstract

We extend the investigation of the recently proposed Kerr/CFT correspondence to large classes of rotating black hole solutions in gauged and ungauged supergravities. The correspondence, proposed originally for four-dimensional Kerr black holes, asserts that the quantum states in the near-horizon region of an extremal rotating black hole are holographically dual to a two-dimensional chiral theory whose Virasoro algebra arises as an asymptotic symmetry of the near-horizon geometry. In fact, in dimension D there are [(D − 1)/2] commuting Virasoro algebras. We consider a general canonical class of near-horizon geometries in arbitrary dimension D, and show that in any such metric the [(D − 1)/2] central charges each imply, via the Cardy formula, a microscopic entropy that agrees with the Bekenstein-Hawking entropy of the associated extremal black hole. In the remainder of the paper we show for most of the known rotating black hole solutions of gauged supergravity, and for the ungauged supergravity solutions with four charges in D = 4 and three charges in D = 5, that their extremal near-horizon geometries indeed lie within the canonical form. This establishes that, in all these examples, the microscopic entropies of the dual CFTs agree with the Bekenstein-Hawking entropies of the extremal rotating black holes.

On the general Kerr/CFT correspondence in arbitrary dimensions

“…This is similar to what happens in the case of extremal Kerr/CFT correspondence [20]. Although we have the same number of Virasoro algebras as that of the azimuthal angles, they are not independent in terms of counting the degrees of freedom for the black hole.…”

Conformal invariance and near-extreme rotating AdS black holes

“…Numerous follow-up papers confirmed the agreement for other extreme rotating black holes. Specifically, this has been verified for extreme four-dimensional KerrNewman (AdS) black holes [4] and for large classes [5] of extreme multicharged rotating black holes in asymptotically Minkowski and AdS space-times, and in diverse dimensions.…”

“…2 In the third section, we turn to the extreme black hole background. The metric in the extreme case, near-horizon regime was studied in [5,29] by taking a specific scaling limit of the general solution. Here we analyze the Klein-Gordon equation, which is a hypergeometric equation with underlying conformal symmetry, and obtain the explicit retarded Green's functions there.…”

More on five dimensional EVH black rings

“…According to [38] one can read the central charge of the dual CFT of the near horizon of the extremal geometry…”