### Abstract

We construct explicit BPS and non-BPS solutions of the U(2k) Yang-Mills equations on the noncommutative space R_{?}^{2n}×S^{2} with finite energy and topological charge. By twisting with a Dirac multi-monopole bundle over S^{2}, we reduce the Donaldson-Uhlenbeck-Yau equations on R_{?}^{2n}×S^{2} 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}×S^{2}. 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}×S^{2}. In the generic case with broken rotational symmetry, we argue that the D0-brane charges on R_{?}^{2n}×S^{2} provide a physical interpretation of the Adams operations in K-theory. © SISSA/ISAS 2003.

Original language | English |
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Pages (from-to) | 505-537 |

Number of pages | 33 |

Journal | Journal of High Energy Physics |

Volume | 7 |

Issue number | 12 |

Publication status | Published - 1 Dec 2003 |

### Keywords

- D-branes
- Integrable Field Theories
- Non-Commutative Geometry
- Solitons Monopoles and Instantons

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## Cite this

*Journal of High Energy Physics*,

*7*(12), 505-537.