Abelianization of Low Energy SU(2) Effective Action

TL;DR

This paper explores the low energy effective action of SU(2) Yang-Mills theory, relating it to a U(1) gauge theory with monopoles, and discusses the connection between the mass parameter and monopole condensate.

Contribution

It introduces a new variable set to relate the SU(2) sigma model to a U(1) gauge theory, providing insights into monopole condensation and the effective action structure.

Findings

Relation between sigma model and U(1) gauge theory established

Connection of mass parameter with monopole condensate discussed

Lattice regularisation leads to compact U(1) gauge theory with electric charges

Abstract

Recently Faddeev and Niemi proposed a low energy effective action for pure SU(2) Yang Mills theory in 4 dimension to describe its long distance physics. The effective action is O(3) $\sigma$ model with a mass parameter, a dimensionless coupling constant e and a topological term. In this work, choosing a new set of variables, we relate this $\sigma$ model to a U(1) gauge theory with electric and magnetic charges of charge e and $4 \pi e^{-1}$ respectively. In the new formulation the connection of the mass parameter with the monopole condensate is discussed. This theory after lattice regularisation is the compact U(1) gauge theory coupled to electric charges.