Deconfinement transition in large-N lattice gauge theory

We study analytically the phase diagram of the pure $SU(N)$ lattice gauge theory at finite temperature, and we attempt to estimate the critical deconfinement temperature. We apply large $N$ techniques to the Wilson and to the Heat Kernel action, and we study the resulting models both in the strong coupling and in the weak coupling limits. Using the Heat Kernel action, we establish an interesting connection between the Douglas-Kazakov phase transition of two-dimensional QCD and the deconfining transition in $d$ dimensions. The analytic results obtained for the critical temperature compare well with Montecarlo simulations of the full theory in $(2+1)$ and in $(3+1)$ dimensions.