Abstract
For a pure gauge theory in three dimensions with a compact, semisimple gauge group, we derive a formula for Creutz ratios of Wilson loops that is valid in the continuum theory to fourth order in the coupling constant. For SU${(2)}_{3}$, we compare this perturbative formula, corrected for periodic boundary conditions, with lattice Creutz ratios that we have measured both in compact simulations guided by Wilson's or Manton's action and in noncompact simulations guided by the Yang-Mills action. The noncompact simulations show no evidence of quark confinement. We also present a critique of compact lattice methods and discuss the renormalization of both compact and noncompact simulations.
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