Instantons and Donaldson-Thomas Invariants

Details Instantons and Donaldson-Thomas Invariants Instantons and Donaldson-Thomas Invariants

2008-04-07

arxiv.org/abs/0804.1087v1

Fortsch.Phys.56:849-855,2008

Physics

High Energy Physics

High Energy Physics - Theory

7 pages, To appear in the proceedings of the RTN workshop "ForcesUniverse", Valencia, October 1-5 2007

Scientific paper

10.1002/prop.200810544

We review some recent progress in understanding the relation between a six dimensional topological Yang-Mills theory and the enumerative geometry of Calabi-Yau threefolds. The gauge theory localizes on generalized instanton solutions and is conjecturally equivalent to Donaldson-Thomas theory. We evaluate the partition function of the U(N) theory in its Coulomb branch on flat space by employing equivariant localization techniques on its noncommutative deformation. Geometrically this corresponds to a higher dimensional generalization of the ADHM formalism. This formalism can be extended to a generic toric Calabi-Yau.

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