$L^2$ geometry of hyperbolic monopoles

Abstract

It is well-known that the $L^2$ metric on the moduli space of hyperbolic monopoles, defined using the Coulomb gauge-fixing condition, diverges. This article shows that an alternative gauge-fixing condition inspired by supersymmetry cures this divergence. The resulting geometry is a hyperbolic analogue of the hyperkähler geometry of Euclidean monopole moduli spaces.

47 pages, no figures v2: Presentation improved in several places. We have also removed a claim that the complex structures are integrable