Magnetic bags in hyperbolic space

Abstract

Reprinted with permission from the American Physical Society: Physical Review D 92, 025052 c (2015) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. A magnetic bag is an Abelian approximation to a large number of coincident SUð2Þ Bogomol'nyiPrasad-Sommerfield 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.

Infinite-Parameter ADHM Transform

“…Another local and infinite-dimensional generalization of the ADHM construction, which on the face of it is quite distinct from the one presented here, involves the Nahm equations with values in the Lie algebra sdiff(S 2 ) of Hamiltonian vector fields on S 2 , and their relation to 'abelian monopole bags' [17,8,10,11,3]. In this case, we have a hodograph transformation which transforms the Nahm equation to the Laplace equation on a domain in R 3 (or in 3-dimensional hyperbolic space).…”

Parabolic Higgs bundles and cyclic monopole chains

“…The magnitude of the scalar field φ is close to zero on the interior of the shell, and seems to attain the value zero at isolated points on the central axis. So these are "cherry bags", in the terminology introduced in [6].…”

Hyperbolic monopoles from hyperbolic vortices

“…Examples of v = 1 2 hyperbolic monopoles which have been studied include those with axial [9] and Platonic [23] symmetry. More recently, monopoles of large charge have been modelled as magnetic bags [5].…”

“…Examples of v = 1 2 hyperbolic monopoles have been obtained from the JNR Ansatz include those with axial [10] and tetrahedral [28] symmetry. Hyperbolic monopoles of large charge have been modelled as magnetic bags in this way [6]. More generally, to obtain the full moduli space of v = 1 2 monopoles, one should use circle-invariant ADHM data, while for half-integer v 1 2 one obtains a discrete version of the Nahm equations, known as the Braam-Austin equations [7].…”