Exact moduli space metrics for hyperbolic vortices

Abstract

Exact metrics on some totally geodesic submanifolds of the moduli space of static hyperbolic N-vortices are derived. These submanifolds, denoted Σ_{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 centre. The geometric properties of Σ_{n,m} are investigated, and it is found that Σ_{n,n-1} is isometric to the hyperbolic plane of curvature -1/(3πn). Geodesic flow on Σ_{n,m}, and a geometrically natural variant of geodesic flow recently proposed by Collie and Tong, are analyzed in detail.

17 pages, 10 figures

References in corpus (4)

• The Dynamics of Chern-Simons Vortices
• The Kähler Potential of Abelian Higgs Vortices
• Schrodinger-Chern-Simons Vortex Dynamics
• Slow equivariant lump dynamics on the two sphere

Cited by in corpus (12)

• On the L^2-metric of vortex moduli spaces
• Manton's five vortex equations from self-duality
• Vortices and magnetic impurities
• The Moduli Space Metric for Well-Separated Non-Abelian Vortices
• Dynamics of Non-Abelian Vortices
• Vortices on Orbifolds
• Ricci magnetic geodesic motion of vortices and lumps
• All Exact Solutions of Non-Abelian Vortices from Yang-Mills Instantons
• BPS Boojums in N=2 supersymmetric gauge theories I
• BPS Boojums in N=2 supersymmetric gauge theories II
• Moduli Spaces of Lumps on Real Projective Space
• Non-abelian vortices on CP^1 and Grassmannians