Electromagnetic Duality in Dyonic RN/CFT Correspondence

TL;DR

This paper explores how electromagnetic duality symmetry in Einstein-Maxwell theory leads to multiple holographic descriptions of dyonic Reissner-Nordström black holes, revealing a rich structure of dualities in black hole thermodynamics.

Contribution

It demonstrates that the $SL(2,Z)$ electromagnetic duality group underpins the multiple holographic pictures of dyonic RN black holes derived from thermodynamics.

Findings

Multiple holographic pictures are generated by $SL(2,Z)$ transformations.

Electromagnetic duality symmetry reflects in the thermodynamics of the black hole.

Thermodynamics encodes the symmetries of the underlying Einstein-Maxwell theory.

Abstract

The area law of Bekenstein-Hawking entropy of the black hole suggests that the black hole should have a lower-dimensional holographic description. It has been found recently that such holographic pictures could be set up from the study of the thermodynamics of both outer and inner horizons for a large class of rotating and charged black holes. For a four-dimensional dyonic Reissner-Nordstr\"om black hole, its thermodynamics indicates that it has multiple holographic pictures not only the electric and magnetic ones corresponding to the conserved electric and magnetic charges carried by the black hole, but also the more generic ones generated by the $SL(2,Z)$ transformations. We show that this $SL(2,Z)$ group originates from the underlying electromagnetic duality symmetry in the Einstein-Maxwell theory. It turns out that the thermodynamics of the black hole not only encodes the information of holographic pictures; moreover it could reflect the symmetries of the underlying theory.