## Abstract

We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U (N) gauge theory on flat space in its Coulomb branch. To evaluate its partition function we use equivariant localization techniques on its noncommutative deformation. As a result the gauge theory localizes on noncommutative instantons which can be classified in terms of N-coloured three-dimensional Young diagrams. We give to these noncommutative instantons a geometrical description in terms of certain stable framed coherent sheaves on projective space by using a higher-dimensional generalization of the ADHM formalism. From this formalism we construct a topological matrix quantum mechanics which computes an index of BPS states and provides an alternative approach to the six-dimensional gauge theory. © 2008 Elsevier B.V. All rights reserved.

Original language | English |
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Pages (from-to) | 452-518 |

Number of pages | 67 |

Journal | Nuclear Physics B |

Volume | 809 |

Issue number | 3 |

DOIs | |

Publication status | Published - 11 Mar 2009 |