Equivariant reduction of Yang–Mills theory over the fuzzy sphere and the emergent vortices Original Research Article

We consider a image Yang–Mills theory on image where image is a Riemannian manifold and image is the fuzzy sphere. Using essentially the representation theory of image we determine the most general image-equivariant gauge field on image. This allows us to reduce the Yang–Mills theory on image down to an Abelian Higgs-type model over image. Depending on the enforcement (or non-enforcement) of a “constraint” term, the latter may (or may not) lead to the standard critically-coupled Abelian Higgs model in the commutative limit, image. For image, we find that the Abelian Higgs-type model admits vortex solutions corresponding to instantons in the original Yang–Mills theory. Vortices are in general no longer BPS, but may attract or repel according to the values of parameters.