Nielsen-Olesen Vortices in Noncommutative Abelian Higgs Model

TL;DR

This paper constructs and analyzes vortex solutions in the noncommutative abelian Higgs model, demonstrating their quantized flux and topological charge, with implications for D-brane physics and noncommutative gauge theories.

Contribution

It introduces explicit vortex solutions in noncommutative gauge theories and explores their topological properties and physical implications, including a novel exact solution in a noncommutative gauge model without a commutative limit.

Findings

Vortex solutions with quantized flux in noncommutative abelian Higgs model.

Explicit computation confirms flux quantization in large and small noncommutativity limits.

Topological charge corresponds to RR charge of BPS D-branes in tachyon condensation context.

Abstract

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 $\theta$ limit as well as in the small $\theta$ limit. In the context of a tachyon vortex on the brane-antibrane 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 left-right-symmetric gauge theory which does not have a commutative limit and construct an exact vortex solution in it.