SU(3)-equivariant quiver gauge theories and nonabelian vortices

We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory on Kähler manifolds of the form M × SU(3)/H, with H = SU(2) × U(1) or H = U(1) × U(1). The induced rank two quiver gauge theories on M are worked out in detail for representations of H which descend from a generic irreducible SU(3)-representation. The reduction of the Donaldson-Uhlenbeck-Yau equations on these spaces induces nonabelian quiver vortex equations on M, which we write down explicitly. When M is a noncommutative deformation of the space ^d, we construct explicit BPS and non-BPS solutions of finite energy for all cases. We compute their topological charges in three different ways and propose a novel interpretation of the configurations as states of D-branes. Our methods and results generalize from SU(3) to any compact Lie group.