Extremal Black Hole/CFT Correspondence in (Gauged) Supergravities

TL;DR

This paper extends the Kerr/CFT correspondence to a broad class of extremal rotating black holes in supergravity theories, showing that their near-horizon geometries' dual CFTs reproduce the black holes' entropies.

Contribution

It generalizes the Kerr/CFT correspondence to higher dimensions and various supergravity solutions, confirming the microscopic entropy matches the Bekenstein-Hawking entropy.

Findings

Microscopic entropies from dual CFTs agree with Bekenstein-Hawking entropies.

Near-horizon geometries of known solutions fit the canonical form.

Multiple Virasoro algebras emerge in higher-dimensional cases.

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.