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.

arXiv commentLatex, 18 pages, minor corrections and references added

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• The Large D Limit of Einstein's Equations
• Rotating black holes and black bars at large D
• Large D gravity and charged membrane dynamics with nonzero cosmological constant
• Island of Reissner-Nordstr$\ddot{\mathbf{o}}$m anti-de Sitter black holes in the large $d$ limit
• Hidden Conformal Symmetries from Killing Towers with an Application to Large-D/CFT
• Large charge operators at large spin from relativistically rotating vortices
• Probing black hole entropy via entanglement
• Hawking radiation from nonrotating singularity-free black holes in conformal gravity