Connection between centre vortices and instantons through gauge-field smoothing

TL;DR

This study demonstrates that centre vortices encode the essential long-range information of SU(3) gauge configurations, linking them to instantons and chiral symmetry breaking through lattice smoothing techniques.

Contribution

It reveals that centre vortices alone can recreate the long-range features of SU(3) gauge theory, establishing a direct connection to instantons and chiral symmetry breaking.

Findings

Centre vortices can generate instanton-like backgrounds after smoothing.

The vortex-based backgrounds reproduce key long-range features of original configurations.

Long-range gauge field structures are contained within centre vortex degrees of freedom.

Abstract

A recent lattice study of the Landau-gauge overlap quark propagator has shown a connection between centre vortices and dynamical chiral symmetry breaking in $\mathrm{SU}(3)$ gauge theory. We further investigate this relationship through an exploration of the connection to the instanton degrees of freedom. After identifying centre vortices on the lattice in maximal centre gauge, we smooth configurations using multiple algorithms. We are able to create an instanton liquid-like background on configurations consisting solely of centre vortices, analogous to that found on Monte-carlo generated configurations after similar smoothing. Through calculations of the static quark potential and Landau-gauge overlap propagator, we show that this background is able to reproduce all salient long-range features of the original configurations. Thus we conclude that the information necessary to recreate the long-range structure of $\mathrm{SU}(3)$ gauge theory is contained within the centre vortex degrees of freedom.