Extremal Static AdS Black Hole/CFT Correspondence in Gauged Supergravities

TL;DR

This paper extends the holographic duality method for calculating black hole entropy to static extremal AdS black holes by using Kaluza-Klein reduction to relate electric charges to internal angular momenta.

Contribution

It introduces a novel approach to include static extremal black holes in the holographic duality framework through Kaluza-Klein sphere reduction.

Findings

Successfully applied to 4-7 dimensional black holes

Reinterpreted electric charges as internal angular momenta

Extended the duality to static extremal black holes

Abstract

A recently proposed holographic duality allows the Bekenstein-Hawking entropy of extremal rotating black holes to be calculated microscopically, by applying the Cardy formula to the two-dimensional chiral CFTs associated with certain reparameterisations of azimuthal angular coordinates in the solutions. The central charges are proportional to the angular momenta of the black hole, and so the method degenerates in the case of static (non-rotating) black holes. We show that the method can be extended to encompass such charged static extremal AdS black holes by using consistent Kaluza-Klein sphere reduction ansatze to lift them to exact solutions in the low-energy limits of string theory or M-theory, where the electric charges become reinterpreted as angular momenta associated with internal rotations in the reduction sphere. We illustrate the procedure for the examples of extremal charged static AdS black holes in four, five, six and seven dimensions.