Universality conditions for the Lorentz invariance of the Wilson loop in the deconfining phase of the Villain gauge theory

We have performed gauge-invariant calculations for a four-dimensional Villain field theory where each orientation of the elementary plaquette carries a different weight E/sub munu/. There are thus six possible E's in four dimensions. This general theory is interesting because the presence of six E's gives us an insight into universality arguments for four-dimensional gauge theories. It is not necessary that the field theory be Lorentz invariant in the presence of six coupling constants E. It may be necessary to impose some restriction on the six E/sub munu/'s to make the field theory Lorentz invariant. In this case we would say that ''conditional universality'' holds. We say that the theory satisfies ''unconditional universality'' if Lorentz invariance holds even if no restrictions are placed on the six E's. We obtain an expression for the Wilson loop in the nonconfining phase of the Villain gauge theory. We find that the Wilson loop is Lorentz invariant despite the fact that no restrictions are placed on the six E's