$L^2$ geometry of hyperbolic monopoles
Differential Geometry
2025-08-07 v2 High Energy Physics - Theory
Abstract
It is well-known that the 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.
Cite
@article{arxiv.2408.07145,
title = {$L^2$ geometry of hyperbolic monopoles},
author = {Guido Franchetti and Derek Harland},
journal= {arXiv preprint arXiv:2408.07145},
year = {2025}
}
Comments
47 pages, no figures v2: Presentation improved in several places. We have also removed a claim that the complex structures are integrable