Gauge independence of Abelian and monopole dominance

TL;DR

This paper introduces a stochastic gauge fixing method to analyze how Abelian projection and monopole contributions to the heavy quark potential depend on gauge choice, finding minimal dependence and supporting monopole's role in confinement.

Contribution

The paper presents a novel stochastic gauge fixing approach allowing continuous gauge variation, demonstrating gauge independence of monopole effects in QCD confinement.

Findings

Abelian contribution to heavy quark potential shows little gauge dependence.

Monopole contribution also exhibits minimal gauge dependence.

Monopole loop length and density are largely gauge independent.

Abstract

We formulate a stochastic gauge fixing method to study the gauge dependence of Abelian projection. In this method, one can change the gauge from the maximally Abelian one to no gauge fixing continuously. We have found that the linear part of the heavy quark potential from Abelian contribution depends little on the gauge parameter. Similar results have been obtained for the monopole contribution part.We also investigate the gauge dependence of the length of monopole loop, which is known to be important for the confinement, and monopole density. These results suggest that the picture that monopole plays an important role for the confinement of QCD dose not depend on choice of the gauge.