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

Understand

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 $T \rightarrow T_d^+$.