Notes on R-charged black holes near criticality and gauge theory

TL;DR

This paper reviews the thermodynamics of R-charged AdS black holes, analyzes their critical behavior, proposes an effective potential for the boundary gauge theory, and computes transport properties like conductivities and diffusion coefficients.

Contribution

It introduces a Bragg-Williams like analysis near critical points and proposes an effective potential for the boundary gauge theory, extending understanding of non-equilibrium phenomena.

Findings

Identification of critical points in R-charged black holes

Proposal of an effective potential for gauge theory

Calculation of conductivities and diffusion coefficients

Abstract

After reviewing the thermodynamics and critical phenomena associated with AdS black holes carrying multiple R-charges in various dimensions, we do a Bragg-Williams like analysis of the systems around its critical points. This leads us to propose an effective potential governing the equilibrium properties of the boundary gauge theory. We also study certain non-equilibrium phenomena associated with these gauge theories. In particular, we compute the conductivities and diffusion coefficients for theories with multiple R-charges in four, three and six dimensions.