R-charged AdS_{5} black holes and large N unitary matrix models

TL;DR

This paper uses AdS/CFT correspondence to relate the thermal phases of R-charged AdS_{5} black holes to the R-charge sector of N=4 gauge theory, revealing phase transitions and critical behavior through an effective matrix model.

Contribution

It introduces an effective unitary matrix model with a logarithmic term to analyze the phase structure of R-charged black holes in AdS_{5} within the gauge/gravity duality.

Findings

Identification of a phase transition point with a cusp catastrophe

Matching of saddle points between supergravity and matrix model

Absence of thermal AdS solution in the R-charged case

Abstract

Using the AdS/CFT, we establish a correspondence between the intricate thermal phases of R-charged AdS_{5} blackholes and the R-charge sector of the N=4 gauge theory, in the large N limit. Integrating out all fields in the gauge theory except the thermal Polyakov line, leads to an effective unitary matrix model. In the canonical ensemble, a logarithmic term is generated in the non-zero charge sector of the matrix model. This term is important to discuss various supergravity properties like i) the non-existence of thermal AdS as a solution, ii) the existence of a point of cusp catastrophe in the phase diagram and iii) the matching of saddle points and the critical exponents of supergravity and those of the effective matrix model.