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Analytic vortex solutions on compact hyperbolic surfaces
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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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Quark confinement consistent with holography due to hyperbolic magnetic monopoles and hyperbolic vortices unifiedly reduced from symmetric instantons
A review showing that symmetric instantons reduce to hyperbolic monopoles and vortices whose dilute gas yields an area law for the Wilson loop, giving a semi-classical, holographic picture of quark confinement.
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