Noncommutative instantons in higher dimensions, vortices and topological K-cycles

We construct explicit BPS and non-BPS solutions of the U(2k) Yang-Millsequations on the noncommutative space R^{2n}_\theta x S^2 with finite energyand topological charge. By twisting with a Dirac multi-monopole bundle overS^2, we reduce the Donaldson-Uhlenbeck-Yau equations on R^{2n}_\theta x S^2 tovortex-type equations for a pair of U(k) gauge fields and a bi-fundamentalscalar field on R^{2n}_\theta. In the SO(3)-invariant case the vortices onR^{2n}_\theta determine multi-instantons on R^{2n}_\theta x S^2. We show thatthese solutions give natural physical realizations of Bott periodicity andvector bundle modification in topological K-homology, and can be interpreted asa blowing-up of D0-branes on R^{2n}_\theta into spherical D2-branes onR^{2n}_\theta x S^2. In the generic case with broken rotational symmetry, weargue that the D0-brane charges on R^{2n}_\theta x S^2 provide a physicalinterpretation of the Adams operations in K-theory.Comment: 1+27 pages; v2: references added, final version to appear in JHE