Equivariant Reduction of Gauge Theories over Fuzzy Extra Dimensions

In SU(N) Yang-Mills theories on a manifold M, which are suitably coupled to a set of scalars, fuzzy spheres may be generated as extra dimensions by spontaneous symmetry breaking. This process results in gauge theories over the product space of the manifold M and the fuzzy spheres with smaller gauge groups. Here we present the SU(2)– and SU(2) × SU(2)-equivariant parametrization of U(2) and U(4) gauge fields on S2F and S2F × S2F respectively and outline the dimensional reduction of these theories over the fuzzy extra dimensions. The emerging dimensionally reduced theories are Higgs type models. Some vortex type solutions of these theories are briefly discussed.