Large-N phase transition in a finite lattice gauge theory

We consider gauge theories of non-Abelian finite groups, and discuss the 1 + 1 dimensional lattice gauge theory of the permutation group S-N as an illustrative example. The partition function at finite N can be written explicitly in a compact form using properties of S-N conjugacy classes. A natural large-N limit exists with a new 't Hooft coupling, lambda = g(2) log N. We identify a Gross-Witten-Wadia-like phase transition at infinite N, at lambda = 2. It is first order. An analog of the string tension can be computed from the Wilson loop expectation value, and it jumps from zero to a finite value. We view this as a type of large-N (de) confinement transition. Our holographic motivations for considering such theories are briefly discussed.