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

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 $\text{n}$ such that ${\text{G}}_{\mu \nu }=G_{\mu \nu }\text{n}$. The first part, $G_{\mu \nu }$, is a space-time tensor and the second part, $\text{n}$, 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.

Comments: 14 pages, 2 figures, Version accepted for publication in PTEP