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We consider a U(2) Yang-Mills theory on M x S_F^2 where M is a Riemannianmanifold and S_F^2 is the fuzzy sphere. Using essentially the representationtheory of SU(2) we determine the most general SU(2)-equivariant gauge field onM x S_F^2. This allows us to reduce the Yang-Mills theory on M x S_F^2 down toan abelian Higgs-type model over M. Depending on the enforcement (ornon-enforcement) of a "constraint" term, the latter may (or may not) lead tothe standard critically-coupled abelian Higgs model in the commutative limit,S_F^2 -> S^2. For M = R^2, we find that the abelian Higgs-type model admitsvortex solutions corresponding to instantons in the original Yang-Mills theory.Vortices are in general no longer BPS, but may attract or repel according tothe values of parameters.

Equivariant reduction of Yang-Mills theory over the fuzzy sphere and the emergent vortices