Instantons on multi-Taub-NUT Spaces II: Bow Construction

Abstract

Unitary anti-self-dual connections on Asymptotically Locally Flat (ALF) hyperk\"ahler 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.