A Near Horizon CFT Dual for Kerr-Newman-$AdS$

TL;DR

This paper demonstrates that the near horizon geometry of Kerr-Newman-AdS black holes is asymptotically AdS2 and is dual to a 1D conformal field theory, reproducing black hole entropy and connecting to Kerr/CFT correspondence.

Contribution

It establishes a duality between the near horizon regime of Kerr-Newman-AdS black holes and a 1D CFT, including derivation of the central charge and entropy matching.

Findings

Central charge reproduces Bekenstein-Hawking entropy via Cardy's formula.

Near horizon geometry is asymptotically AdS2 and dual to a 1D CFT.

Agreement with Kerr/CFT correspondence in appropriate limits.

Abstract

We show that the near horizon regime of a Kerr-Newman-$AdS$ (KN$AdS$) black hole, given by its two dimensional analogue $a la$ Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303), is asymptotically $AdS_2$ and dual to a one dimensional quantum conformal field theory (CFT). The s-wave contribution of the resulting CFT's energy-momentum-tensor together with the asymptotic symmetries, generate a centrally extended Virasoro algebra, whose central charge reproduces the Bekenstein-Hawking entropy via Cardy's Formula. Our derived central charge also agrees with the near extremal Kerr/CFT Correspondence (2009 Phys. Rev. D 80, 124008) in the appropriate limits. We also compute the Hawking temperature of the KN$AdS$ black hole by coupling its Robinson and Wilczek two dimensional analogue (RW2DA) to conformal matter.