### A D Popov and R J Szabo

#### Abstract

We construct explicit BPS and non-BPS solutions of the Yang-Mills equations on the noncommutative space $R^{2n}_\theta\times S^2$ which have manifest rotational symmetry . Using SU(2)-equivariant dimensional reduction techniques, we show that the solutions imply an equivalence between instantons on $R^{2n}_\theta\times S^2$ and nonabelian vortices on $R^{2n}_\theta$, which can be interpreted as a blowing-up of a chain of D0-branes on $R^{2n}_\theta$ into a chain of spherical D2-branes on $R^{2n}_\theta\times S^2$. 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.