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

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.