Connections between Thin,Thick and Projection Vortices in SU(2) Lattice Gauge Theory

TL;DR

This paper explores the relationship between different vortex configurations in SU(2) lattice gauge theory, demonstrating how projection vortices can be exactly identified and related to other formulations without approximation.

Contribution

It establishes a direct connection between SO(3) × Z(2) and SU(2) configurations and shows that projection vortices occur exactly in the maximal center gauge.

Findings

Projection vortices occur without approximation in the maximal center gauge.

Dropping a factor in the Wilson loop expression leads to the vortex dominance approximation.

A direct link between Kovacs-Tomboulis and projection vortex formulations is demonstrated.

Abstract

We elucidate the connection between $SO(3) \times Z(2)$ and the usual SU(2) configuration variables. By exploiting the freedom of choosing a particular SO(3) representative we find a direct connection between the two configuration spaces. We are then able to compare the Kovacs-Tomboulis formulation of center vortices with the projection vortex formulation on the same configuration. Choosing a different representative, and going to the maximal center gauge, we show that projection vortices occur without approximation. The projection vortex dominance approximation results from dropping a factor in an exact expression for the Wilson loop.