Abelian Projection of Massive SU(2) Yang-Mills Theory

TL;DR

This paper derives an effective Abelian gauge theory from a modified SU(2) Yang-Mills framework with mass terms, demonstrating Abelian dominance, a composite potential, and connections to the Skyrme-Faddeev model.

Contribution

It introduces a gauge fixing method that preserves SU(2) symmetry and derives an effective theory showing confinement-related potentials and topological models.

Findings

Derivation of an effective Abelian gauge theory with mass terms

Identification of a composite Yukawa and linear potential

Connection of the effective theory to the Skyrme-Faddeev model

Abstract

We derive an effective Abelian gauge theory (EAGT) of a modified SU(2) Yang-Mills theory. The modification is made by explicitly introducing mass terms of the off-diagonal gluon fields into pure SU(2) Yang-Mills theory, in order that Abelian dominance at a long-distance scale is realized in the modified theory. In deriving the EAGT, the off-diagonal gluon fields involving longitudinal modes are treated as fields that produce quantum effects on the diagonal gluon field and other fields relevant at a long-distance scale. Unlike earlier papers, a necessary gauge fixing is carried out without spoiling the global SU(2) gauge symmetry. We show that the EAGT allows a composite of the Yukawa and the linear potentials which also occurs in an extended dual Abelian Higgs model. This composite potential is understood to be a static potential between color-electric charges. In addition, we point out that the EAGT involves the Skyrme-Faddeev model.