Phases of Zn lattice gauge theory.

Abstract

We use the Lagrangian formulation of the Zx gauge theory in four dimensions and demonstrate its equivalence with the partition function for a Coulomb gas of electric and magnetic- loops. This model is shown to be self-dual when expressed in the Villain form. It is found, as a lower bound that for N < 4 there are only two phases related by duality, while for N > 4 three phases appear. The explicit calculation of the Wilson loop identifies them as electric confining, nonconfining and magnetic confining.