Nielsen–Olesen vortices in noncommutative space

We construct an exact regular vortex solution to the self-dual equations of the Abelian Higgs model in noncommutative space for arbitrary values of θ. 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.