Magnetic bags in hyperbolic space

TL;DR

This paper explores magnetic bags in hyperbolic space, deriving their Nahm transform, and compares their approximation accuracy for different monopole configurations, highlighting the limitations of abelian models and proposing a non-abelian extension.

Contribution

It introduces the Nahm transform for magnetic bags in hyperbolic space and proposes a non-abelian extension to better approximate spherical monopoles.

Findings

Magnetic bags in hyperbolic space can be constructed for large N.

The magnetic disc accurately models axially symmetric monopoles.

A non-abelian interior improves approximation for spherical monopoles.

Abstract

A magnetic bag is an abelian approximation to a large number of coincident SU(2) BPS monopoles. In this paper we consider magnetic bags in hyperbolic space and derive their Nahm transform from the large charge limit of the discrete Nahm equation for hyperbolic monopoles. An advantage of studying magnetic bags in hyperbolic space, rather than Euclidean space, is that a range of exact charge N hyperbolic monopoles can be constructed, for arbitrarily large values of N, and compared with the magnetic bag approximation. We show that a particular magnetic bag (the magnetic disc) provides a good description of the axially symmetric N-monopole. However, an abelian magnetic bag is not a good approximation to a roughly spherical N-monopole that has more than N zeros of the Higgs field. We introduce an extension of the magnetic bag that does provide a good approximation to such monopoles and involves a spherical non-abelian interior for the bag, in addition to the conventional abelian exterior.