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Equivariant reduction of U(4) gauge theory over S-F(2) x S-F(2) and the emergent vortices

We consider a U(4) Yang-Mills theory on M x S-F(2) x S-F(2) where M is an arbitrary Riemannian manifold and S-F(2) x S-F(2) is the product of two fuzzy spheres spontaneously generated from a SU(N) Yang-Mills theory on M which is suitably coupled to six scalars in the adjoint of U(N). We determine the SU(2) x SU(2)-equivariant U(4) gauge fields and perform the dimensional reduction of the theory over S-F(2) x S-F(2). The emergent model is a U(1)(4) gauge theory coupled to four complex and eight real scalar fields. We study this theory on R-2 and find that, in certain limits, it admits vortex type solutions with U(1)(3) gauge symmetry and discuss some of their properties.