Holographic Duals of Black Holes in Five-dimensional Minimal Supergravity

TL;DR

This paper explores the holographic duality between extremal black holes in five-dimensional supergravity and conformal field theories, calculating key quantities like the Virasoro algebra, central charge, and entropy, confirming the duality's consistency.

Contribution

It provides explicit calculations of the dual CFT's Virasoro algebra, central charge, and entropy for five-dimensional extremal black holes, revealing proportionality to angular momentum and symmetry properties.

Findings

CFT entropy matches Bekenstein-Hawking entropy

Central charges proportional to angular momentum components

Rotational symmetry relates dual CFTs for different black holes

Abstract

We examine the dual conformal field theory for extremal charged black holes in five-dimensional minimal supergravity with 2 independent angular momenta. The conformal field theory Virasoro algebra, central charge, and temperature are calculated. Additionally the conformal field theory entropy is calculated using the Cardy formula and agrees with the Bekenstein-Hawking black hole entropy. The central charges are directly proportional to the angular momentum components of the black hole. In five and higher dimensions, rotations of the spacetime correspond to rotations of the central charges leading to an apparent symmetry relating the conformal field theories dual to each black hole. A rotationally invariant central charge, which is proportional to the total angular momentum, is used to discuss the supersymmetric BMPV black hole limits.