RN/CFT Correspondence From Thermodynamics

TL;DR

This paper refines the thermodynamics approach to holographically describe Reissner-Nordström black holes in various dimensions, establishing dual CFTs and exploring magnetic and dyonic dualities through symmetry transformations.

Contribution

It introduces a refined thermodynamics method with a quantization condition to accurately determine the dual CFT central charges for RN black holes, including novel magnetic and dyonic dual pictures.

Findings

Derived holographic duals for RN black holes in arbitrary dimensions.

Confirmed dual CFT descriptions via asymptotic symmetry and hidden conformal symmetry.

Discovered a new magnetic dual picture for four-dimensional dyonic RN black holes.

Abstract

Recent studies suggest that in the Kerr/CFT correspondence, much universal information of the dual CFT, including the central charges and the temperatures, is fully encoded in the thermodynamics of the outer and inner horizons of the Kerr(-Newman) black holes. In this paper, we study holographic descriptions of Reissner-Nordstr\"om (RN) black holes in arbitrary dimensions by using the thermodynamics method.We refine the thermodynamics method proposed in arXiv:1206.2015 by imposing the "quantization" condition so that we can fix the ambiguity in determining the central charges of the dual CFT of RN black holes. Using the refined thermodynamics method, we find the holographic CFT duals for the RN black holes, and confirm these pictures by using conventional analysis of asymptotic symmetry group and the hidden conformal symmetry in the low-frequency scattering. In particular, we revisit the four-dimensional dyonic RN black hole and find a novel magnetic picture, besides the known electric CFT dual picture. We show how to generate a class of dual dyonic pictures by $SL(2,Z)$ transformations.