5D Extremal Rotating Black Holes and CFT duals

TL;DR

This paper explores the dual conformal field theories (CFTs) associated with 5D extremal rotating black holes, revealing a modular symmetry that links various CFT duals and confirms their entropy matches the Bekenstein-Hawking entropy.

Contribution

It demonstrates the existence of an SL(2,Z) modular group acting on the near horizon geometry, generating a lattice of dual CFTs with consistent entropy calculations.

Findings

Identified an SL(2,Z) symmetry in the near horizon geometry.

Established a lattice of dual CFTs related by modular transformations.

Confirmed the microscopic entropy matches the Bekenstein-Hawking entropy.

Abstract

Kerr/CFT correspondence has been recently applied to various types of 5D extremal rotating black holes. A common feature of all such examples is the existence of two chiral CFT duals corresponding to the U(1) symmetries of the near horizon geometry. In this paper, by studying the moduli space of the near horizon metric of five dimensional extremal black holes which are asymptotically flat or AdS, we realize an SL(2,Z) modular group which is a symmetry of the near horizon geometry. We show that there is a lattice of chiral CFT duals corresponding to the moduli points identified under the action of the modular group. The microscopic entropy corresponding to all such CFTs are equivalent and are in agreement with the Bekenstein-Hawking entropy.