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Exact moduli space metrics for hyperbolic vortex polygons

Krusch, Steffen, Speight, J.Martin (2010) Exact moduli space metrics for hyperbolic vortex polygons. Journal of Mathematical Physics, 51 (2). 022304-022316. ISSN 0022-2488. (doi:10.1063/1.3277189) (KAR id:23722)


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
DOI/Identification number: 10.1063/1.3277189
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: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Steffen Krusch
Date Deposited: 09 Jul 2010 08:40 UTC
Last Modified: 16 Nov 2021 10:02 UTC
Resource URI: (The current URI for this page, for reference purposes)

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