CFT Duals for Extreme Black Holes

TL;DR

This paper proposes a holographic duality between extremal black holes and two-dimensional CFTs, deriving central charges and temperatures, and confirming the microscopic entropy matches the Bekenstein-Hawking law, with extensions to higher dimensions.

Contribution

It generalizes the Kerr/CFT correspondence to a broader class of extremal black holes, including those with charge and cosmological constant, and introduces a second dual CFT in the Reissner-Nordstrom limit.

Findings

Asymptotic symmetries form a Virasoro algebra.

Derived semiclassical formulas for central charge and temperature.

Microscopic entropy matches the Bekenstein-Hawking entropy.

Abstract

It is argued that the general four-dimensional extremal Kerr-Newman-AdS-dS black hole is holographically dual to a (chiral half of a) two-dimensional CFT, generalizing an argument given recently for the special case of extremal Kerr. Specifically, the asymptotic symmetries of the near-horizon region of the general extremal black hole are shown to be generated by a Virasoro algebra. Semiclassical formulae are derived for the central charge and temperature of the dual CFT as functions of the cosmological constant, Newton's constant and the black hole charges and spin. We then show, assuming the Cardy formula, that the microscopic entropy of the dual CFT precisely reproduces the macroscopic Bekenstein-Hawking area law. This CFT description becomes singular in the extreme Reissner-Nordstrom limit where the black hole has no spin. At this point a second dual CFT description is proposed in which the global part of the U(1) gauge symmetry is promoted to a Virasoro algebra. This second description is also found to reproduce the area law. Various further generalizations including higher dimensions are discussed.