Quiver gauge theory of non-Abelian vortices and noncommutative instantons in higher dimensions

We construct explicit Bogomolnyi, Prasad, Sommerfeld (BPS) and non-BPS solutions of the Yang-Mills equations on the noncommutative space Rθ 2n × S2 which have manifest spherical symmetry. Using SU(2)-equivariant dimensional reduction techniques, we show that the solutions imply an equivalence between instantons on Rθ 2n × S2 and non-Abelian vortices on Rθ 2n, which can be interpreted as a blowing-up of a chain of D0 -branes on Rθ 2n into a chain of spherical D2 -branes on Rθ 2n × S2. The low-energy dynamics of these configurations is described by a quiver gauge theory which can be formulated in terms of new geometrical objects generalizing superconnections. This formalism enables the explicit assignment of D0 -brane charges in equivariant K -theory to the instanton solutions.