Non-abelian vortices on compact Riemann surfaces

Abstract

We consider the vortex equations for a U(n) gauge field coupled to a Higgs field with values on the n times n square matrices. It is known that when these equations are defined on a compact Riemann surface, their moduli space of solutions is closely related to a moduli space of tau-stable holomorphic n-pairs on that surface. Using this fact and a local factorization result for the Higgs matrix, we show that the vortex solutions are entirely characterized by (1) the location in the surface of the zeros of the determinant of the Higgs matrix and (2) by the choice of a vortex internal structure at each of these zeros. We describe explicitly the vortex internal spaces and show that they are compact and connected spaces.

17 pages; v2: typos corrected, as will appear in CMP

References in corpus (6)

• Solitons in the Higgs phase -- the moduli matrix approach --
• Non-Abelian Vortices of Higher Winding Numbers
• Non-Abelian Semilocal Strings in N=2 Supersymmetric QCD
• On the moduli space of semilocal strings and lumps
• Constructing Non-Abelian Vortices with Arbitrary Gauge Groups
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• Geometry and Energy of Non-abelian Vortices
• Vortices on Orbifolds
• Dimensional reduction over the quantum sphere and non-abelian q-vortices
• The Volume of the Quiver Vortex Moduli Space
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• Moduli Spaces of Abelian Vortices on Kahler Manifolds
• Non-abelian vortices, Hecke modifications and singular monopoles
• Pairs of pants, Pochhammer curves and $L^2$-invariants
• Non-abelian vortices on CP^1 and Grassmannians