Maximally non-abelian vortices from self-dual Yang–Mills fields

Abstract

A particular dimensional reduction of SU(2N) Yang–Mills theory on Σ×S2, with Σ a Riemann surface, yields an S(U(N)×U(N)) gauge theory on Σ, with a matrix Higgs field. The SU(2N) self-dual Yang–Mills equations reduce to Bogomolny equations for vortices on Σ. These equations are formally integrable if Σ is the hyperbolic plane, and we present a subclass of solutions.