Matrix Models and AdS/CFT
Vinay Rajendra Patil
IISER, Bhopal, India
According to AdS/CFT correspondence, different phases of large N gauge theories correspond to different phases of asymptotically AdS black holes. While the thermal partition function of large N SU(N) gauge theory on a compact manifold S3xS1 reduces to an integral over a Unitary matrix, the phase structure of the unitary matrix models describing the theory then admits a dual description in terms of thermodynamics of asymptotic AdS black holes.
Using Schwinger-Dyson equations, we study the phase structure of the unitary matrix models describing the theory in zero ‘t Hooft coupling limit. We characterize the distinct phases in terms of the gaps in the eigenvalue density. We first consider the approximated model with the leading term of the effective action. We show that, the theory undergoes a first-order transition between gapped phases and the phase with uniform eigenvalue density. As the theory allows higher-order terms, we then evaluate the contribution of the term of order TrU2TrU†2. In this model, we find that the qualitative phase structure consists of five different phases, a no-gap phase, two one gap phases and two two gap phases. Under the duality, these phases then demand a description as distinct phases of the AdS black hole.
