Phase structure of U( N→∞) gauge theory on a two-dimensional lattice for a broad class of variant actions

Abstract

It is pointed out that finding the partition function for U( N) gauge theory on a two-dimensional lattice in the limit N→∞ reduces, for a broad class of single-plaquette actions, to a well-known and solved mathematical problem. The case where in the single plaquette action the matrix U + U + occuring in Wilson's formula is replaced by an arbitrary polynomial in this matrix, is discussed in detail and explicit results for the second-order polynomial are presented. A rich phase structure with second- and third-order phase transitions is found. The results are shown to have at the qualitative level a simple thermodynamical interpretation. They support the view that the phase structure of a lattice gauge theory is an artifact of the lattice action used rather than some reflection of the underlying group structure.