Non-abelian vortices on compact Riemann surfaces

Details Non-abelian vortices on compact Riemann surfaces Non-abelian vortices on compact Riemann surfaces

2008-10-17

arxiv.org/abs/0810.3220v2

Commun.Math.Phys.291:799-812,2009

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1007/s00220-009-0838-9

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.

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