Extremal Black Hole/CFT Correspondence in (Gauged) Supergravities

TL;DR

This work generalizes the Kerr/CFT correspondence to a wide class of extremal rotating black holes across gauged and ungauged supergravity theories in multiple dimensions. By showing that near-horizon geometries of extremal solutions can be cast into a canonical form supporting multiple commuting Virasoro algebras, the authors derive central charges and Frolov--Thorne temperatures that reproduce the Bekenstein--Hawking entropy via the Cardy formula. They verify the mechanism across explicit 4D and 5D examples and extend the analysis to higher dimensions (up to 7D and beyond), demonstrating consistent microscopic entropies for dual CFTs. The results strongly support a universal, dimensionality-agnostic Kerr/CFT-like holographic description for extremal rotating black holes in a broad swath of supergravity theories, with potential implications for quantum gravity and holography in diverse spacetimes.

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.