Yang-Mills Instantons, Quivers and Bows

The study of hyperkaehler manifolds of lowest dimension (and of gauge theory on them) leads to a chain of generalizations of the notion of a quiver: quivers, bows, slings, and monowalls. This talk focuses on bows, their representations, and solutions. In particular, we formulate a complete construction of Yang-Mills instantons on Asymptotically Locally Flat (ALF) spaces.

We begin by generalizing Uhlenbeck's theorem to the ALF case and computing the index of the instanton Dirac operator. We formulate the bow construction of instantons and demonstrate that it is complete. This work is done in collaboration with Andres Larrain-Hubach and Mark Stern.

Time permitting, we use this bow construction to describe instanton moduli space as a slice of the space of curves in Tℙ1TP1. This leads to an explicit expression for the Kaehler potential on the instanton moduli space.



University of Arizona; Member, School of Mathematics