Analytic vortex solutions on compact hyperbolic surfaces (1502.01990v1)

Published 6 Feb 2015 in hep-th, math-ph, math.MP, and nlin.SI

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.

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