Eigenvalue repulsion in an effective theory of SU(2) Wilson lines in three dimensions

TL;DR

This paper investigates the eigenvalue behavior of SU(2) Wilson lines in three dimensions through simulations, revealing eigenvalue repulsion near the deconfining transition and the emergence of a Z(N) symmetric vacuum in the confined phase.

Contribution

It introduces a non-perturbative fuzzy-bag term into the effective theory, demonstrating its impact on eigenvalue distributions and phase structure.

Findings

Eigenvalue repulsion occurs above the deconfining transition.

The eigenvalue repulsion region diminishes at very weak coupling.

A Z(N) symmetric vacuum appears in the confined phase.

Abstract

We perform simulations of an effective theory of SU(2) Wilson lines in three dimensions. We include a non-perturbative "fuzzy-bag" contribution which is added to the one-loop perturbative potential for the Wilson line. We confirm that, at moderately weak coupling, this leads to eigenvalue repulsion in a finite region above the deconfining phase transition which shrinks in the extreme weak-coupling limit. A non-trivial Z(N) symmetric vacuum arises in the confined phase.