Another Realization of Kerr/CFT Correspondence

TL;DR

This paper presents a new realization of the Kerr/CFT correspondence by imposing stronger asymptotic boundary conditions on the Kerr near-horizon geometry, yielding an asymptotic symmetry that contains all exact isometries and promoting the SL(2,R) sector to a Virasoro algebra. Although the asymptotic-charge algebra has vanishing central extension, anomalies emerge when using a quasi-local boundary energy–momentum tensor, enabling finite-temperature analysis and a mapping to a chiral CFT. Finite-temperature corrections to mass and angular momentum are derived from these anomalies, and the Cardy entropy reproduces the extremal and near-extremal Kerr data if the boundary cutoff Λ is tied to the near-extremality parameter ε via Λ ∝ ε^−1. The work clarifies the role of boundary terms and regularization in holographic Kerr/CFT and suggests paths for refining the dual description of deviations from extremality.

Abstract

We study another realization of the Kerr/CFT correspondence. By imposing new asymptotic conditions for the near horizon geometry of Kerr black hole, an asymptotic symmetry which contains all of the exact isometries can be obtained. In particular, the Virasoro algebra can be realized as an enhancement of SL(2,R) symmetry of the AdS geometry. By using this asymptotic symmetry, we discuss finite temperature effects and show the correspondence concretely.