Kerr-AdS/CFT Correspondence in Diverse Dimensions

TL;DR

The paper generalizes the Kerr/CFT correspondence to extremal Kerr–AdS black holes across dimensions 4 through 7 and beyond, showing that the near-horizon Virasoro symmetries yield a microscopic entropy via the Cardy formula that precisely matches the Bekenstein–Hawking entropy. In 4D, a single chiral CFT with central charge $c_L$ reproduces the extremal Kerr–AdS entropy through $S=\tfrac{1}{3}\pi^2 c_L T_L$ with a finite left-moving temperature $T_L$ and $T_R=0$; in 5D (and higher) each independent rotation defines its own chiral CFT with central charge $c_{\phi_i}$ and temperature $T_{\phi_i}$, yet all yield the same macroscopic entropy. The authors provide explicit near-horizon geometries, central charges, and Frolov–Thorne temperatures for the cases studied and verify the entropy match in dimensions 4–7, including higher-dimensional formulations. This work strengthens the Kerr/CFT framework and highlights a consistent picture of holography for extremal rotating black holes with or without a cosmological constant, while suggesting a rich structure of dual CFTs tied to the angular momenta.

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.