SU(3) lattice gauge theory in 4 dimensions with a modified Wilson action

Abstract

The Wilson action for the 4-d gauge theory involves the trace in the fundamental representation of the product of link variables on lattice plaquettes. By computer simulation, we study an extension of this action with an additional term involving the plaquette trace in the adjoint representation. The gauge group is SU(3). We find a phase structure similar to that found recently for SU(2) with such an action. In particular, we find a first order transition in the SU(3)/Z(3) gauge theory and a critical endpoint close to the so-called crossover region for the Wilson action. We also study a 648 element subgroup of SU(3) to see whether it might be sufficient to simulate the continuum limit of the SU(3) theory. We find that, even with the extended action, the freezing transition from the discreteness of this subgroup precludes this possibility. Using an abalogy with the Potts model, we approximate the phase diagram for an even bigger subgroup of SU(3), one with 1080 elements. We find that this group is also not dense enough to describe the SU(3) continuum limit with the extended action.