Matching of Wilson loop eigenvalue densities in 1+1, 2+1 and 3+1 dimensions

We investigate the matching of eigenvalue densities of Wilson loops in SU(N) lattice gauge theory: the eigenvalue densities in 1+1, 2+1 and 3+1 dimensions are nearly identical when the traces of the loops are equal. We show that the matching is present to at least second order in the strong–coupling expansion, and also to second order in perturbation theory. We find that in the continuum limit there is matching at all values of the trace for bare Wilson loops. We confirm numerically that there is matching in these limits and find there are small violations away from them. We discuss the implications for the bulk transitions and for non–analytic gap formation at N = ∞ in 2+1 and 3+1 dimensions.