Phase diagram of mixed lattice gauge theory from the viewpoint of large N

Abstract

It is shown how the mixed SU( N)−SU( N)/Z( N) lattice gauge theory (LGT) can be solved in the large- N limit if the solution of the standard (Wilson) LGT is known. The method is exemplified by the two-dimensional case where the exact solution of the standard U(∞) LGT is known. For finite N the method is justified by the approximation of factorization. In four dimensions this method is used to obtain the phase diagram of the mixed LGT taking the plaquette energy and the specific heat of the standard LGT from the Monte Carlo data. For N = 3, 4, 5 the obtained phase diagrams are predictions, while for N = 2 a comparison with the Bhanot-Creutz results is presented. It is shown that corrections to factorization [O(1/ N 2)] do not spoil the qualitative results. The exact formula relating the slope of the phase transition line to the value of the plaquette energy is presented. The significance of the large− N phase transitions in the mixed LGT for the understanding of the confining mechanism in the continuum is discussed.