A hyper-Kähler metric on the moduli spaces of monopoles with arbitrary symmetry breaking

Abstract

We construct the hyper-Kähler moduli space of framed monopoles over R3 for any connected, simply connected, compact, semisimple Lie group and arbitrary mass and charge, and hence arbitrary symmetry breaking. In order to do so, we define a configuration space of pairs with appropriate asymptotic conditions and perform an infinite-dimensional quotient construction. We make use of the b and scattering calculuses to study the relevant differential operators.