Nielsen-Olesen vortices in noncommutative space

TL;DR

This paper constructs an exact vortex solution in noncommutative space for the Abelian Higgs model, extending classical Nielsen-Olesen vortices to a noncommutative setting with arbitrary noncommutativity parameter.

Contribution

It introduces a novel ansatz in Fock space that yields exact regular vortex solutions in noncommutative space for all values of the noncommutativity parameter.

Findings

Derived exact vortex solutions in noncommutative space.

Computed flux and energy of the solutions.

Discussed properties and implications of the solutions.

Abstract

We construct an exact regular vortex solution to the self-dual equations of the Abelian Higgs model in non-commutative space for arbitrary values of $\theta$. To this end, we propose an ansatz which is the analogous, in Fock space, to the one leading to exact solutions for the Nielsen-Olesen vortex in commutative space. We compute the flux and energy of the solution and discuss its relevant properties.