# 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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