Maximally Non-Abelian Vortices from Self-dual Yang--Mills Fields

Understand

A particular dimensional reduction of SU(2N) Yang--Mills theory on $\Sigma \times S^2$, with $\Sigma$ a Riemann surface, yields an $S(U(N) \times U(N))$ gauge theory on $\Sigma$, with a matrix Higgs field.

• The SU(2N) self-dual Yang--Mills equations reduce to Bogomolny equations for vortices on $\Sigma$.
• These equations are formally integrable if $\Sigma$ is the hyperbolic plane, and we present a subclass of solutions.