CFT dual of charged AdS black hole in the large dimension limit

Abstract

We study the dual CFT description of the $d+1$-dimensional Reissner-Nordström-Anti de Sitter (RN-AdS${}_{d+1}$) black hole in the large dimension (large $d$) limit, both for the extremal and nonextremal cases. The central charge of the dual CFT${}_2$ (or chiral CFT${}_1$) is calculated for the near horizon near extremal geometry which possess an AdS${}_2$ structure. Besides, the $Q$-picture hidden conformal symmetry in the nonextremal background can be naturally obtained by a probe charged scalar field in the large $d$ limit, without the need to input the usual limits to probe the hidden conformal symmetry. Furthermore, an new dual CFT description of the nonextremal RN-AdS${}_{d+1}$ black hole is found in the large $d$ limit and the duality is analyzed by comparing the entropies, the absorption cross sections and the retarded Green's functions obtained both from the gravity and the dual CFT sides.

Latex, 18 pages, minor corrections and references added