Centre vortex geometry at finite temperature

TL;DR

This paper investigates how the geometry of centre vortices in SU(3) gauge theory changes at finite temperature, revealing structural shifts associated with the deconfinement phase transition.

Contribution

It provides a detailed analysis of vortex structure alterations across the phase transition, including visualizations and statistical measures, highlighting key geometric and behavioural changes.

Findings

Vortex sheets prefer the temporal direction above the critical temperature.

Branching point clustering at short distances disappears at high temperatures.

Vortex behavior shifts indicate loss of confinement during deconfinement.

Abstract

The geometry of centre vortices is studied in $\mathrm{SU(3)}$ gauge theory at finite temperature to capture the key structural changes that occur through the deconfinement phase transition. Visualisations of the vortex structure in temporal and spatial slices of the lattice reveal a preference for the vortex sheet to align with the temporal dimension above the critical temperature. This is quantified through a correlation measure. A collection of vortex statistics, including vortex and branching point densities, and vortex path lengths between branching points, are analysed to highlight internal shifts in vortex behaviour arising from the loss of confinement. We find the zero-temperature inclination of branching points to cluster at short distances vanishes at high temperatures, embodying a rearrangement of branching points within the vortex structure. These findings establish the many aspects of centre vortex geometry that characterise the deconfinement phase transition in pure gauge theory.