Abelianization of Low Energy SU(2) Effective Action

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) $σ$ 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 $σ$ model to a U(1) gauge theory with electric and magnetic charges of charge e and $4 πe^{-1}$ 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.