We construct explicit BPS and non-BPS solutions of the U(2k) Yang-Mills equations on the noncommutative space R?2n×S2 with finite energy and topological charge. By twisting with a Dirac multi-monopole bundle over S2, we reduce the Donaldson-Uhlenbeck-Yau equations on R?2n×S2 to vortex-type equations for a pair of U(k) gauge fields and a bi-fundamental scalar field on R?2n. In the SO(3)-invariant case the vortices on R ?2n determine multi-instantons on R?2n×S2. We show that these solutions give natural physical realizations of Bott periodicity and vector bundle modification in topological K-homology, and can be interpreted as a blowing-up of D0-branes on R?2n into spherical D2-branes on R?2n×S2. In the generic case with broken rotational symmetry, we argue that the D0-brane charges on R?2n×S2 provide a physical interpretation of the Adams operations in K-theory. © SISSA/ISAS 2003.
|Number of pages||33|
|Journal||Journal of High Energy Physics|
|Publication status||Published - 1 Dec 2003|
- Integrable Field Theories
- Non-Commutative Geometry
- Solitons Monopoles and Instantons