Instantons and Donaldson–Thomas invariants

✍ Scribed by M. Cirafici; A. Sinkovics; R.J. Szabo

• Book ID: 105357700
• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 173 KB
• Volume: 56
• Category: Article
• ISSN: 0015-8208
• DOI: 10.1002/prop.200810544

✦ Synopsis

Abstract

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.