Vortex configurations in SO(3) \times Z(2)

TL;DR

This paper investigates the configuration space of the Tomboulis $SO(3) imes Z(2)$ formulation, focusing on constraints from monopoles and boundary conditions, and proposes an algorithm for efficient updates.

Contribution

It introduces a new update algorithm that respects the constraints of the $SO(3) imes Z(2)$ model with periodic boundary conditions.

Findings

The configuration space is characterized by monopole constraints.

An efficient algorithm for constrained updates is proposed.

The approach facilitates studies of the model's properties.

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. Furthermore, there is an additional constraint coming from the boundary conditions. We propose an update algorithm that satisfies the constraints and is straightforward to implement.