On Holographic Dual of the Dyonic Reissner-Nordstr\"om Black Hole

TL;DR

This paper demonstrates that the non-extremal dyonic Reissner-Nordström black hole exhibits hidden conformal symmetry, indicating a dual 2D conformal field theory description, supported by matching physical quantities from gravity and CFT perspectives.

Contribution

It reveals hidden conformal symmetry in the non-extremal dyonic Reissner-Nordström black hole and derives dual CFT parameters without higher-dimensional embedding.

Findings

Hidden conformal symmetry probed by scalar field at low frequencies

Exact dual CFT parameters obtained without 5D embedding

Matching of absorption cross sections and correlators supports duality

Abstract

It is shown that the hidden conformal symmetry, namely $SO(2,2) \sim SL(2,R)_L \times SL(2,R)_R$ symmetry, of the non-extremal dyonic Reissner-Nordstr\"om black hole can be probed by a charged massless scalar field at low frequencies. The existence of such hidden conformal symmetry suggests that the field theory holographically dual to the 4D Reissner-Nordstr\"om black hole indeed should be a 2D CFT. Although the associated AdS$_3$ structure does not explicitly appear in the near horizon geometry, the primary parameters of the dual CFT$_2$ can be exactly obtained without the necessity of embedding the 4D Reissner-Nordstr\"om black hole into 5D spacetime. The duality is further supported by comparing the absorption cross sections and real-time correlators obtained from both the CFT and the gravity sides.