Simulations in SO(3) \times Z(2) lattice gauge theory

TL;DR

This paper investigates vortex structures in SO(3) x Z(2) lattice gauge theory through simulations, measuring gauge-invariant vortex counters and comparing different vortex detection methods to understand their role in gauge invariance.

Contribution

It introduces a simulation approach in the SO(3) x Z(2) formulation and compares gauge-invariant vortex counters with projection vortex counters in lattice gauge theory.

Findings

Gauge-invariant vortex counters effectively identify vortex linkages.

Comparison shows differences between gauge-invariant and projection vortex detection.

Results enhance understanding of vortex roles in non-Abelian gauge theories.

Abstract

We explore simulations on periodic lattices in the Tomboulis $SO(3) \times Z(2)$ formulation. We measure gauge invariant vortex counters for "thin", "thick" and "hybrid" vortex sheets in order to tag Wilson loops by the occurance of gauge invariant vortices linking them. We also measure projection vortex counters defined in the maximal center gauge for comparison.