A Note on Charged Black Holes in AdS space and the Dual Gauge Theories

TL;DR

This paper investigates the thermodynamics and phase structures of charged black holes in Anti-de Sitter space, proposing effective potentials for dual gauge theories based on off-shell free energies.

Contribution

It introduces off-shell free energies and effective potentials for charged black holes in AdS space and their dual gauge theories, providing a new framework for analyzing phase structures.

Findings

Identification of equilibrium phases via saddle points

Construction of off-shell free energies from action-derived thermodynamics

Proposal of effective potentials for boundary gauge theories

Abstract

We study the thermodynamics and the phase structures of Reissner-Nordstrom and Born-Infeld black holes in AdS space by constructing ``off-shell'' free energies using thermodynamic quantities derived directly from the action. We then use these results to propose ``off-shell'' effective potentials for the respective boundary gauge theories. The saddle points of the potentials describe all the equilibrium phases of the gauge theories.