R-charged AdS₅ black holes and large N unitary matrix models

Abstract

Using the anti-de Sitter (AdS)/conformal field theories correspondence, we establish a correspondence between the intricate thermal phases of R-charged AdS₅ black holes 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 nonzero charge sector of the matrix model. This term is important for discussing various supergravity properties like (i) the non-existence of a thermal AdS phase 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.