U(1) effective confinement theory from SU(2) restricted gauge theory via the Julia-Toulouse Approach

TL;DR

This paper derives an abelian effective theory for color confinement in SU(2) gauge theory using the Julia-Toulouse approach, highlighting monopole condensation and resulting in a model with Yukawa and linear confinement interactions.

Contribution

It introduces a novel application of the Julia-Toulouse approach to derive an effective U(1) theory from SU(2) gauge theory, emphasizing topological and monopole effects.

Findings

Effective U(1) theory exhibits Yukawa and linear confinement interactions.

Monopole condensation leads to a phase dominated by magnetic condensate.

The approach connects topological defects with confinement mechanisms.

Abstract

We derive an U(1) effective theory of color confinement by applying the so-called Julia-Toulouse Approach for defects condensation to the SU(2) restricted gauge theory defined by means of the Cho decomposition of the non-abelian connection. Cho's geometric construction naturally displays the topological degrees of freedom of the theory and can be used to put the Yang-Mills action into an abelianized form under certain conditions. On the other hand, the use of the Julia-Toulouse prescription to deal with the monopole condensation leads to an effective action describing the phase whose dynamics is dominated by the magnetic condensate. The effective theory we found describes the interaction between external electric currents displaying a short-range Yukawa interaction plus a linear confinement term that governs the long distance physics.