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

We study the dual CFT description of the $d+1$-dimensional Reissner-Nordstr\"om-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.