Vortices in $SO(3)\times Z(2)$ simulations

TL;DR

This paper investigates vortex configurations in $SO(3) imes Z(2)$ lattice simulations, introducing a new constrained update algorithm and analyzing boundary condition effects on the configuration space.

Contribution

It presents a novel update algorithm for constrained variables in $SO(3) imes Z(2)$ lattice simulations and examines boundary condition impacts.

Findings

Proposed a straightforward constrained update algorithm.

Analyzed boundary condition effects on configuration space.

Demonstrated the algorithm's applicability in simulations.

Abstract

We explore simulations on periodic lattices in the Tomboulis $SO(3)\times Z(2)$ formulation. The dynamical variables are constrained. We propose an update algorithm that satisfies the constraints and is straightforward to implement. We show how boundary conditions put constraints on the configuration space.