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Physical Review D

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

Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany

Phys. Rev. D 76, 034503 – Published 13 August, 2007

DOI: https://doi.org/10.1103/PhysRevD.76.034503

Abstract

We investigate the matching of eigenvalue densities of Wilson loops in $S U (N)$ 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 that there are small violations away from them. We discuss the implications for the bulk transitions and for nonanalytic gap formation at $N = \infty$ in $2 + 1$ and $3 + 1$ dimensions.

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