Variational analysis of lattice gauge theories

A variational approach to the study of four-dimensional lattice gauge theories is initiated. We illustrate the technique by first analyzing the simpler SU (2) chiral model. A systematic treatment of the SU (2) lattice gauge theory with a mixed fundamental-adjoint action is presented next. This leads to an improvement over the standard mean-field (MF) results; in particular, a "second-order deconfining transition line" in the negative SO (3) coupling region previously identified by a MF technique now disappears. All transitions found are first order. The procedure is then generalized to the large-$N$ limit. In particular, a first-order transition line corresponding to the breaking of a (local) U (1) symmetry (at vanishing fundamental coupling) is again identified.