R-charged AdS_{5} black holes and large N unitary matrix models
  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. 
Pallab Basu, Spenta R. Wadia