SU(2) versus SU(2)/Z2 lattice gauge theory and the crossover from weak to strong coupling

We point out that, for weak coupling, the SU(2) lattice gauge theory can be shown to be dominated by an embedded SU(2)/Z2 theory. We propose that the behavior of the SU(2) model in the crossover region is a remnant of the activity of the underlying SU(2)/Z2 theory which shows a phase transition. Such behavior is related to the presence of Z2-monopoles in these theories. We emphasize that modifications of the lattice action, that are innocuous for β → infinity, can appreciably change the detailed structure of the crossover region. (orig.)