Fractal Dimension of Gauge-fixing Defects

TL;DR

This paper investigates the fractal dimension of gauge-fixing defects in lattice SU(3) gluodynamics, revealing phase-dependent clustering behavior in Landau gauge and contrasting behavior in maximal Abelian gauge.

Contribution

It introduces a method to compute the fractal dimension of gauge-fixing defects and compares clustering properties across different gauges and temperature phases.

Findings

Landau gauge sites form 1D clusters in the confining phase

Cluster dimensionality decreases above the critical temperature

MA gauge resistant sites do not show significant clustering

Abstract

The fractal dimension $D_f$ of sites resisting Landau or maximal Abelian(MA) gauge fixing in lattice $SU(3)$ gluodynamics is defined and computed. In Landau gauge such sites clump into $D_f\sim 1$ clusters in the confining phase. In the finite temperature phase their dimensionality drops to $D_f < 1$, that is, clustering seems to dissipate. In contrast, MA gauge resistant sites fail to exhibit a notable tendency to cluster at any temperature.