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Gauge Theories with Fuzzy Extra Dimensions and Noncommutative Vortices and Fluxons

A U(2) Yang-Mills theory on the space M × S 2 F is considered, where it is assumed that M is an arbitrary noncommutative space and S 2 F is a fuzzy sphere spontaneously generated from a noncommutative U(N ) Yang-Mills theory on M coupled to a triplet of scalars in the adjoint of U(N ). SU(2)-equivariant reduction of this theory leads to a noncommutative U(1) gauge theory coupled adjointly to a set of scalar fields. The emergent model is studied on the Groenewald-Moyal plane R 2 θ and it is found that, in certain limits, it admits noncommutative, non-BPS vortex as well as fluxon solutions.