Gross-Witten-Wadia transition in a matrix model of deconfinement

We study the deconfining phase transition at nonzero temperature in a SU(N) gauge theory, using a matrix model which was analyzed previously at small N. We show that the model is soluble at infinite N, and exhibits a Gross-Witten-Wadia transition. In some ways, the deconfining phase transition is of first order: at a temperature $T_d$, the Polyakov loop jumps discontinuously from 0 to1/2, and there is a nonzero latent heat $\sim N^2$. In other ways, the transition is of second order: e.g., the specific heat diverges as $C \sim 1/(T-T_d)^{3/5}$ when $T \rightarrow T_d^+$. Other critical exponents satisfy the usual scaling relations of a second order phase transition. In the presence of a nonzero background field $h$ for the Polyakov loop, there is a phase transition at the temperature $T_h$ where the value of the loop =1/2, with $T_h < T_d$. Since $\partial C/\partial T \sim 1/(T-T_h)^{1/2}$ as $T \rightarrow T_h^+$, this transition is of third order.