Vortices and monopole distributions in $Z(2) \times SO(3)$ lattice gauge theory

TL;DR

This paper investigates the distribution of vortices and monopoles in Z(2) and SO(3) lattice gauge theories using a gauge-invariant formulation to better understand the flux tube structure and the area law.

Contribution

It introduces a gauge-invariant approach using Tomboulis formulation to analyze vortices and monopoles in lattice gauge theory, providing new observables for flux tube studies.

Findings

Identification of vortex and monopole distributions near Wilson loops

Insights into the flux tube structure and area law behavior

Development of gauge-invariant observables for lattice gauge analysis

Abstract

We examine the occurance of Z(2) and SO(3) vorticies and monopole distributions in the neighborhood of Wilson loops. We use the Tomboulis formulation, equivalent to the Wilson action, in which the links are invariant under Z(2) transformations and new plaquette variables carry the Z(2) degrees of freedom. This gives new gauge invariant observables to help gain insight into the area law and structure of the flux tube.