$L^2$ 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 hyperk\"ahler geometry of Euclidean monopole moduli spaces.