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We construct explicit BPS and non-BPS solutions of the Yang-Mills equationson the noncommutative space R^{2n}_\theta x S^2 which have manifest sphericalsymmetry. Using SU(2)-equivariant dimensional reduction techniques, we showthat the solutions imply an equivalence between instantons on R^{2n}_\theta xS^2 and nonabelian vortices on R^{2n}_\theta, which can be interpreted as ablowing-up of a chain of D0-branes on R^{2n}_\theta into a chain of sphericalD2-branes on R^{2n} x S^2. The low-energy dynamics of these configurations isdescribed by a quiver gauge theory which can be formulated in terms of newgeometrical objects generalizing superconnections. This formalism enables theexplicit assignment of D0-brane charges in equivariant K-theory to theinstanton solutions.Comment: 45 pages, 4 figures; v2: minor correction

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