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arXiv · 2408.07145

$L^2$ geometry of hyperbolic monopoles

Guido Franchetti·Derek Harland
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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.

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Guido Franchetti, Derek Harland. 2024-08-13. $L^2$ geometry of hyperbolic monopoles. https://arxiv.org/abs/2408.07145

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