## Abstract

We consider equivariant dimensional reduction of Yang-Mills theory on Kähler manifolds of the form M × CP^{1} × CP^{1}. This induces a rank two quiver gauge theory on M which can be formulated as a Yang-Mills theory of graded connections on M. The reduction of the Yang-Mills equations on M × CP^{1} × CP^{1} induces quiver gauge theory equations on M and quiver vortex equations in the BPS sector. When M is the noncommutative space R_{?}^{2n} both BPS and non-BPS solutions are obtained, and interpreted as states of D-branes. Using the graded connection formalism, we assign D0-brane charges in equivariant K-theory to the quiver vortex configurations. Some categorical properties of these quiver brane configurations are also described in terms of the corresponding quiver representations. © SISSA 2006.

Original language | English |
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Article number | 054 |

Journal | Journal of High Energy Physics |

Volume | 2006 |

Issue number | 9 |

DOIs | |

Publication status | Published - 1 Sep 2006 |

## Keywords

- Brane Dynamics in Gauge Theories
- Non-Commutative Geometry
- Solitons Monopoles and Instantons