Non-Abelian Stokes theorem and quark confinement in QCD

TL;DR

This paper reformulates the non-Abelian Wilson loop using a non-Abelian Stokes theorem to explore Abelian dominance and magnetic monopoles in low-energy QCD, proposing a modified gauge fixing that induces gluon and ghost mass generation.

Contribution

It introduces a modified maximal Abelian gauge and demonstrates mass generation for off-diagonal gluons and ghosts while preserving asymptotic freedom.

Findings

Off-diagonal gluons acquire mass through ghost condensation.

Ghost-anti-ghost condensation occurs due to four ghost interactions.

Asymptotic freedom remains intact in the modified gauge.

Abstract

To understand the Abelian dominance and magnetic monopole dominance in low-energy QCD, we rewrite the non-Abelian Wilson loop into the form which is written in terms of its Abelian components or the 't Hooft-Polyakov tensor describing the magnetic monopole. This is peformed by making use of a version of non-Abelian Stokes theorem. We propose a modified version of the maximal Abelian (MA) gauge. By adopting the modified MA gauge in QCD, we show that the off-diagonal gluons and Faddeev-Popov ghosts acquire their masses through the ghost--anti-ghost condensation due to four ghost interaction coming from the gauge-fixing term of the modified MA gauge. The asymptotic freedom of the original non-Abelian gauge theory is preserved in this derivation.