Gauge Theories with Fuzzy Extra Dimensions and Noncommutative Vortices and Fluxons

A U (2) Yang-Mills theory on the space M x S2F is considered, where it is assumed that M is an arbitrary noncommutative space and S2F 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 R2θ and it is found that, in certain limits, it admits noncommutative, non-BPS vortex as well as fluxon solutions.