Abelian Dominance in Wilson Loops

TL;DR

This paper provides evidence that the Abelian projection in QCD, defined without gauge fixing, captures the essential gauge potential responsible for confinement, supporting the Abelian dominance hypothesis in Wilson loops.

Contribution

It introduces a gauge independent definition of Abelian projection and demonstrates its dominance in Wilson loop integrals, advancing understanding of confinement mechanisms.

Findings

Abelian projection without gauge fixing suffices for Wilson loop calculations

Gauge potential in Wilson loops is exactly the Abelian projected component

Supports the Abelian dominance hypothesis in QCD confinement

Abstract

It has been conjectured that the Abelian projection of QCD is responsible for the confinement of color. Using a gauge independent definition of the Abelian projection which does {\it not} employ any gauge fixing, we provide a strong evidence for the Abelian dominance in Wilson loop integral. In specific we prove that the gauge potential which contributes to the Wilson loop integral is precisely the one restricted by the Abelian projection.