Branching of Center Vortices in SU(3) Lattice Gauge Theory

TL;DR

This study investigates the behavior of center vortex branching in SU(3) lattice gauge theory, revealing its potential as an indicator of the deconfinement phase transition and its independence from lattice spacing within the studied range.

Contribution

It introduces a normalized branching probability measure in SU(3) Yang-Mills theory that signals the deconfinement transition and is unaffected by lattice spacing variations.

Findings

Branching probability is independent of lattice spacing in the studied window.

Rapid change in branching probability at the deconfinement transition.

Branching probability effectively indicates the critical temperature and vortex re-arrangement.

Abstract

We analyze the branching of center vortices in $SU(3)$ Yang-Mills theory in maximal center gauge. When properly normalized, we can define a branching probability that turns out to be independent of the lattice spacing (in the limited scaling window studied here). The branching probability shows a rapid change at the deconfinement phase transition which is much more pronounced in space slices of the lattice as compared to time slices. Though not a strict order parameter (in the sense that it vanishes in one phase) the branching probability is thus found to be a reliable indicator for both the location of the critical temperature and the geometric re-arrangement of vortex matter across the deconfinement phase transition.