Wilson loops with oppositely oriented plaquettes as a probe of center vortex structure

TL;DR

This paper investigates Wilson loops with oppositely oriented plaquettes to probe center vortex structures in lattice gauge theory, revealing behaviors consistent with vortex models and highlighting complex orientation effects.

Contribution

It introduces a novel Wilson loop observable with opposite plaquettes and demonstrates its effectiveness in probing vortex structures, including unexpected deviations explained by a new vortex model.

Findings

Vertical configuration aligns with vortex picture expectations.

Parallel configuration shows deviations from naive area-law.

A simple vortex model explains the observed effects.

Abstract

We study Wilson loops with a nontrivial orientation structure in lattice gauge theory as a probe of the center vortex picture. The observable is a single Wilson loop containing two plaquettes with opposite orientations, realized in two geometries referred to as the vertical and parallel configurations. The vertical case behaves consistently with expectations from the vortex picture. In contrast, the parallel configuration shows a deviation from the naive area-law expectation which cannot be explained solely by the opposite orientations of the plaquettes. We introduce a simple qualitative vortex model which accounts for this behavior and shows that the observed effect can still be understood within the vortex framework.