Geometry of Periodic Monopoles

Maldonado, R.; Ward, R.S.

Abstract

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.

Citation

Maldonado, R., & Ward, R. (2013). Geometry of Periodic Monopoles. Physical Review D, 88(12), Article 125013. https://doi.org/10.1103/physrevd.88.125013

• Journal Article Type: Article
• Publication Date: Dec 6, 2013
• Deposit Date: Oct 28, 2013
• Publicly Available Date: Dec 13, 2013
• Journal: Physical Review D - Particles, Fields, Gravitation, and Cosmology
• Print ISSN: 1550-7998
• Electronic ISSN: 1550-2368
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 88
• Issue: 12
• Article Number: 125013
• DOI: https://doi.org/10.1103/physrevd.88.125013
• Public URL: https://durham-repository.worktribe.com/output/1445137