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Yang-Mills Instantons in Curved Backgrounds

S. Cherkis (Trinity)

28.05.2009 at 16:15 

Instanton constructions of Atiyah, Drinfeld, Hitchin, and Manin and of Nahm provide general self-dual Yang-Mills solutions on flat spaces, namely on R4 and on R3xS1 respectively. Quiver construction of Kronheimer and Nakajima generalizes the ADHM construction to provide instantons on ALE spaces, which are deformations of finite quotients of the flat R4. We generalize these constructions to obtain instantons on any Asymptotically Locally Flat self-dual gravitational instantons. These are essentially curved backgrounds. The data in our construction is encoded in terms of Bow Diagrams, which generalize Quivers. As an illustration of this Bow formalism we find explicit expression for a single instanton on the Taub-NUT space as well as the metric on its moduli space. Time permitting, we also discuss the twistor description and compact integral expressions for these instantons.

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