Gauge Invariance and Confinement in Noncompact Simulations of Su(2)

In 1980 Creutz [1] displayed quark confinement at moderate coupling in lattice simulations of both abelian and nonabelian gauge theories. Whether nonabelian confinement is as much an artifact of Wilson’s action as is abelian confinement remains unclear. The basic variables of Wilson’s formulation [2] are elements of a compact group and enter the action only through traces of their products. The Wilson action has false vacua [3] which affect the string tension [4,5]. In simulations of SU(2) with gauge-invariant potential barriers between the true vacuum and the false vacua, the string tension has been seen to drop [4] or even vanish[5]. To examine these questions, some physicists have introduced lattice actions that are noncompact discretizations of the continuum action with fields as the basic variables. For U(1) these noncompact formulations are accurate for all coupling strengths [6]; for SU(2) they agree well with perturbation theory at very weak coupling [7]. This report relates the results of measuring Wilson loops at strong coupling, β ≡ 4/g = 0.5, on a 12 lattice in a noncompact simulation of SU(2) gauge theory without gauge fixing or fermions. In this simulation the fields are subjected to random compact gauge transformations which restore a semblance of lattice gauge invariance.