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Geometry of Periodic Monopoles

Maldonado, R.; Ward, R.S.

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R. Maldonado

R.S. Ward


Bogomol’nyi-Prasad-Sommerfield monopoles on R 2 ×S 1 correspond, via the generalized Nahm transform, to certain solutions of the Hitchin equations on the cylinder R×S 1 . The moduli space M of two monopoles with their center of mass fixed is a four-dimensional manifold with a natural hyperkähler metric, and its geodesics correspond to slow-motion monopole scattering. The purpose of this paper is to study the geometry of M in terms of the Nahm-Hitchin data, i.e., in terms of structures on R×S 1 . In particular, we identify the moduli, derive the asymptotic metric on M , and discuss several geodesic surfaces and geodesics on M . The latter include novel examples of monopole dynamics.


Maldonado, R., & Ward, R. (2013). Geometry of Periodic Monopoles. Physical Review D, 88(12), Article 125013.

Journal Article Type Article
Publication Date Dec 6, 2013
Deposit Date Oct 28, 2013
Publicly Available Date Dec 13, 2013
Journal Physical Review D
Print ISSN 1550-7998
Electronic ISSN 1550-2368
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 88
Issue 12
Article Number 125013


Published Journal Article (1.3 Mb)

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Copyright Statement
Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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