Non-abelian vortices on the torus

Abstract

We study periodic arrays of non-Abelian vortices in an SU(N) × U(1) gauge theory with Nf flavors of fundamental matter multiplets. We carefully discuss the corresponding twisted boundary conditions on the torus and propose an ansatz to solve the first order Bogomolnyi equations which we find by looking to a bound of the energy. We solve the equations numerically and construct explicit vortex solutions.