Nielsen-Olesen Vortices in Noncommutative Abelian Higgs Model

We construct Nielsen-Olesen vortex solution in the noncommutative abelian Higgs model. We derive the quantized topological flux of the vortex solution. We find that the flux is integral by explicit computation in the large θ limit as well as in the small θ limit. In the context of a tachyon vortex on the braneantibrane system we demonstrate that it is this topological charge that gives rise to the RR charge of the resulting BPS D-brane. We also consider the leftright-symmetric gauge theory which does not have a commutative limit and construct an exact vortex solution in it. July 2000 e-mail: [email protected], [email protected], [email protected]