Exact moduli space metrics for hyperbolic vortex polygons

Krusch, Steffen and Speight, J.Martin (2010) Exact moduli space metrics for hyperbolic vortex polygons. Journal of Mathematical Physics, 51 (2). 022304-022316. ISSN 0022-2488 . (Full text available)

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http://dx.doi.org/10.1063/1.3277189

Abstract

Exact metrics on some totally geodesic submanifolds of the moduli space of static hyperbolic N-vortices are derived. These submanifolds, denoted as Sigma_{n,m}, are spaces of C_n-invariant vortex configurations with n single vortices at the vertices of a regular polygon and m=N−n coincident vortices at the polygon's center. The geometric properties of Sigma_{n,m} are investigated, and it is found that Sigma_{n,n−1} is isometric to the hyperbolic plane of curvature −(3 pi n)^{−1}. The geodesic flow on Sigma_{n,m} and a geometrically natural variant of geodesic flow recently proposed by Collie and Tong [“The dynamics of Chern-Simons vortices,” Phys. Rev. D Part. Fields Gravit. Cosmol. 78, 065013 (2008);e-print arXiv:hep-th/0805.0602] are analyzed in detail.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science) > QA440 Geometry
Q Science > QC Physics > QC20 Mathematical Physics
Q Science > QC Physics > QC174.12 Quantum theory > QC174.26.W28 Topological solitons
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Steffen Krusch
Date Deposited: 09 Jul 2010 08:40
Last Modified: 18 Jul 2014 08:30
Resource URI: http://kar.kent.ac.uk/id/eprint/23722 (The current URI for this page, for reference purposes)
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