Symmetric hyperbolic monopoles

Cockburn, Alexander

doi:10.1088/1751-8113/47/39/395401

Cited by 10 publications

(15 citation statements)

References 17 publications

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“…The bulk of the research on symmetric monopoles however concerned monopoles with discrete group of symmetries in [7-9, 18-22, 31, 37-40]. Everything cited so far takes place on the Euclidean space, but symmetries should be useful wherever there are some, and have been exploited for studying monopoles on the hyperbolic 3-space in [4,11,27,30,36], and for studying monopole chains, that is monopoles on R 2 × S 1 in [14].…”

Section: Background and Motivationmentioning

confidence: 99%

Construction of Nahm data and BPS monopoles with continuous symmetries

Charbonneau,

Dayaprema,

Lang

et al. 2021

Preprint

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Section: Background and Motivationmentioning

confidence: 99%

Construction of Nahm data and BPS monopoles with continuous symmetries

Charbonneau,

Dayaprema,

Lang

et al. 2021

Preprint

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“…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].…”

Section: Hyperbolic Monopolesmentioning

confidence: 99%

Hyperbolic monopoles from hyperbolic vortices

Maldonado

2017

Nonlinearity

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Certain hyperbolic monopoles and all hyperbolic vortices can be constructed from SO(2) and SO(3) invariant Euclidean instantons, respectively. This observation allows us to describe a large class of hyperbolic monopoles as hyperbolic vortices embedded into H 3 and yields a remarkably simple relation between the two Higgs fields. This correspondence between vortices and monopoles gives new insight into the geometry of the spectral curve and the moduli space of hyperbolic monopoles. It also allows an explicit construction of the fields of a hyperbolic monopole invariant under a Z action, which we compare to periodic monopoles in Euclidean space. * R.Maldonado@damtp.cam.ac.uk arXiv:1508.07304v1 [hep-th]

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“…Naively, it might be expected that placing N + 1 points on the vertices of a regular (N + 1)-gon in an equatorial circle would produce a monopole with a discrete cyclic symmetry, but the fact that all the points lie on a circle enhances the cyclic symmetry to an axial symmetry. For later reference, in the plane X 3 = 0 the length of the Higgs field has the simple expression [18]…”

Section: Exact Hyperbolic Monopoles With Large Chargementioning

confidence: 99%

Magnetic bags in hyperbolic space

2015

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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.

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Symmetric hyperbolic monopoles

Cited by 10 publications

References 17 publications

Construction of Nahm data and BPS monopoles with continuous symmetries

Construction of Nahm data and BPS monopoles with continuous symmetries

Hyperbolic monopoles from hyperbolic vortices

Magnetic bags in hyperbolic space

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