Center vortex properties in the Laplace center gauge of SU(2) Yang-Mills theory

TL;DR

This paper compares vortex properties in SU(2) Yang-Mills theory using Laplace and Maximal-center gauges, revealing differences in vortex densities and the limitations of vortex gas models in the continuum limit.

Contribution

It provides a detailed analysis of vortex densities in different gauges and highlights the inadequacy of vortex gas approximations in the continuum limit.

Findings

In MCG, vortex densities are physical in the continuum.

In LCG, vortex piercing and crossing points become dense in the continuum.

Vortex gas models are insufficient to describe the observed phenomena.

Abstract

Resorting to the the Laplace center gauge (LCG) and to the Maximal-center gauge (MCG), respectively, confining vortices are defined by center projection in either case. Vortex properties are investigated in the continuum limit of SU(2) lattice gauge theory. The vortex (area) density and the density of vortex crossing points are investigated. In the case of MCG, both densities are physical quantities in the continuum limit. By contrast, in the LCG the piercing as well as the crossing points lie dense in the continuum limit. In both cases, an approximate treatment by means of a weakly interacting vortex gas is not appropriate.