The phase structure of two dimensional pure U(N) lattice gauge theories with complex action

We study the phase structure of two dimensional pure lattice gauge theory with a Chern term. The symmetry groups are non-Abelian,finite and disconnected sub-groups of SU(3). Since the action is imaginary it introduces a rich phase structure compared to the originally trivial two dimensional pure gauge theory. The Z3 group is the center of these groups and the result shows that if we use one dimensional irreducible representations (irreps) for group elements the phase diagrams are similar to diagrams of Z3 group. Other irreps with different dimensionality show a little different behaviour for the phase diagram. The phase transition for the Z3 group is first order. The phase structure of the U(N) model is considered and it is proved that it has an infinite number of first order phase transitions.