Kerr-AdS/CFT Correspondence in Diverse Dimensions

TL;DR

This paper extends the Kerr/CFT correspondence to extremal Kerr-AdS black holes across multiple dimensions, showing that microscopic CFT entropy matches Bekenstein-Hawking entropy in these cases.

Contribution

It generalizes the Kerr/CFT duality to higher-dimensional extremal Kerr-AdS black holes, providing explicit entropy comparisons and formulas for all dimensions.

Findings

Microscopic and Bekenstein-Hawking entropies agree for 4D Kerr-AdS.

Agreement extends to 5, 6, and 7 dimensions.

General formulas for higher dimensions are derived.

Abstract

It was proposed recently that the near-horizon states of an extremal four-dimensional Kerr black hole could be identified with a certain chiral conformal field theory whose Virasoro algebra arises as an asymptotic symmetry algebra of the near-horizon Kerr geometry. Supportive evidence for the proposed duality came from the equality of the microscopic entropy of the CFT, calculated by means of the Cardy formula, and the Bekenstein-Hawking entropy of the extremal Kerr black hole. In this paper we examine the proposed Kerr/CFT correspondence in a broader context. In particular, we show that the microscopic entropy and the Bekenstein-Hawking entropy agree also for the extremal Kerr-AdS metric in four dimensions, and also for the extremal Kerr-AdS metrics in dimensions 5, 6 and 7. General formulae for all higher dimensions are also presented.