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Geometry of periodic monopoles.

Maldonado, R. and Ward, R.S. (2013) 'Geometry of periodic monopoles.', Physical review D., 88 (12). p. 125013.


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.

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Publisher 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.
Date accepted:No date available
Date deposited:13 December 2013
Date of first online publication:November 2013
Date first made open access:No date available

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