Non-Abelian Vortices on the Torus

TL;DR

This paper investigates non-Abelian vortex solutions on a torus within an SU(N) x U(1) gauge theory, introducing twisted boundary conditions, proposing an ansatz, and numerically constructing explicit solutions.

Contribution

It presents a novel approach to solving Bogomolnyi equations for non-Abelian vortices on a torus with twisted boundary conditions, including explicit numerical solutions.

Findings

Derived twisted boundary conditions for vortices on a torus

Proposed an ansatz to solve Bogomolnyi equations

Constructed explicit vortex solutions numerically

Abstract

We study periodic arrays of non-Abelian vortices in an $SU(N) \times U(1)$ gauge theory with $N_f$ 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.