A hyper-K\"ahler metric on the moduli space of monopoles with arbitrary symmetry breaking

Author:

Jaime Mendizabal

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Mathematical Physics (math-ph)

journal:

date:

2023-06-04 16:00:00

Abstract

We construct the hyper-K\"ahler moduli space of framed monopoles over $\mathbb{R}^3$ for any connected, simply connected, compact, semisimple Lie group and arbitrary mass and charge, and hence symmetry breaking. In order to do so, we define a configuration space of pairs with appropriate asymptotic conditions and perform an infinite-dimensional quotient construction. We make use of the b and scattering calculuses to study the relevant differential operators.

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