English

$L^2$ geometry of hyperbolic monopoles

Differential Geometry 2025-08-07 v2 High Energy Physics - Theory

Abstract

It is well-known that the L2L^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.

Keywords

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

R2 v1 2026-06-28T18:12:12.564Z