Vortices in SO(3)xZ(2) simulations

TL;DR

This paper investigates the configuration space of an $SO(3) imes Z(2)$ gauge theory, proposing an update algorithm that respects constraints and analyzing vortex structures through various gauge-invariant counters.

Contribution

It introduces a new update algorithm for the $SO(3) imes Z(2)$ formulation that satisfies all constraints and explores vortex configurations with detailed measurements.

Findings

The proposed algorithm reaches all configurations within the constrained space.

Boundary conditions significantly influence the configuration space.

Gauge-invariant vortex counters reveal different vortex characteristics.

Abstract

We study the configuration space of the Tomboulis $SO(3) \times Z(2)$ formulation with periodic boundary conditions. The dynamical variables are constrained by the required coincidence of Z(2) and SO(3) monopoles. We propose an update algorithm that satisfies the constraints and is straightforward to implement. We further prove that this it reaches all configurations. We show how the boundary conditions put constraints on the configuration space. We measure gauge invariant vortex counters for "thin", "thick" and "hybrid" vortex sheets. For comparison we also measure projection vortex counters defined in the maximal center gauge.