Instantons on multi-taub-nut spaces ii: bow construction

Abstract

Unitary anti-self-dual connections on Asymptotically Locally Flat (ALF) hyperkähler spaces are constructed in terms of data organized in a bow. Bows generalize quivers, and the relevant bow gives rise to the underlying ALF space as the moduli space of its particular representation—the small representation. Any other representation of that bow gives rise to anti-self-dual connections on that ALF space.

We prove that each resulting connection has finite action, i.e. it is an instanton. Moreover, we derive the asymptotic form of such a connection and compute its topological class.