Exact moduli space metrics for hyperbolic vortex polygons
- School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury CT2 7NF (United Kingdom)
- Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT (United Kingdom)
Exact metrics on some totally geodesic submanifolds of the moduli space of static hyperbolic N-vortices are derived. These submanifolds, denoted as {sigma}{sub n,m}, are spaces of C{sub 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}{sub n,m} are investigated, and it is found that {sigma}{sub n,n-1} is isometric to the hyperbolic plane of curvature -(3{pi}n){sup -1}. The geodesic flow on {sigma}{sub 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.
- OSTI ID:
- 21335909
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 2 Vol. 51; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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