Analytic vortex solutions on compact hyperbolic surfaces

Abstract

We construct, for the first time, Abelian-Higgs vortices on certain compact surfaces of constant negative curvature. Such surfaces are represented by a tessellation of the hyperbolic plane by regular polygons. The Higgs field is given implicitly in terms of Schwarz triangle functions and analytic solutions are available for certain highly symmetric configurations.

21 pages, 6 figures

References in corpus (6)

• Integrability of Vortex Equations on Riemann Surfaces
• Non-Abelian Vortices on Riemann Surfaces: an Integrable Case
• Integrable vortex-type equations on the two-sphere
• Vortices as degenerate metrics
• Vortex solutions of the Popov equations
• Two-parametric hyperbolic octagons and reduced Teichmueller space in genus two

Cited by in corpus (7)

• Toroidal and Elliptic Quiver BPS Algebras and Beyond
• Integrable Abelian Vortex-like solitons
• Five Vortex Equations
• Hyperbolic vortices and Dirac fields in 2+1 dimensions
• Generalized Maxwell-Higgs vortices in models with enhanced symmetry
• Kähler quantization of vortex moduli
• The Berry connection of the Ginzburg-Landau vortices