Appearance of vortices and monopoles in a decomposition of an SU(2) Yang-Mills field

TL;DR

This paper demonstrates how vortices and monopoles emerge as topological solitons in the low energy limit of SU(2) Yang-Mills theory through a specific field decomposition motivated by Abelian dominance.

Contribution

It introduces a decomposition of the SU(2) Yang-Mills field in the infrared regime that reveals the emergence of vortices and monopoles as topological solitons.

Findings

Vortices and monopoles appear as topological solitons in the low energy limit.

Decomposition leads to an Abelian gauge field coupled to a scalar field.

Scalar field influences monopole configurations.

Abstract

We show how vortices can appear in the low energy limit of a pure SU(2) Yang-Mills theory as topological solitons. Motivated by Abelian dominance, we suppose that in the infrared regime of the SU(2) Yang-Mills theory, the field strength tensor can be obtained by multiplying two parts: $ G_{\mu\nu} $ and $ \textbf{n} $ such that $ \textbf{G}_{\mu\nu}=G_{\mu\nu} \textbf{n} $. The first part, $ G_{\mu\nu} $, is a space-time tensor and the second part, $ \textbf{n} $, is an isotriplet unit vector field which gives the Abelian direction at each space-time point. This leads to a decomposition for the SU(2) Yang-Mills field in the infrared regime. We show that vortices as well as monopoles can appear as a result of this decomposition where we have started with a pure Yang-Mills theory and we have ended up with a theory with an Abelian gauge field coupled to a scalar field. The effect of this scalar field on monopoles is also discussed.