NS5-Branes, T-Duality and Worldsheet Instantons

TL;DR

This paper re-examines the T-duality between NS5-branes and ALF spaces, revealing that multi-worldsheet instantons localize the NS5-brane, breaking isometry and providing new insights into vortex solutions.

Contribution

It demonstrates that instanton effects correct the dualized NS5-brane metric, leading to localization and new predictions for vortex asymptotics.

Findings

Instantons break the target space isometry.

NS5-brane becomes localized after instanton corrections.

Predicted exponential decay coefficient of BPS vortex solutions.

Abstract

The equivalence of NS5-branes and ALF spaces under T-duality is well known. However, a naive application of T-duality transforms the ALF space into a smeared NS5-brane, de-localized on the dual, transverse, circle. In this paper we re-examine this duality, starting from a two-dimensional N=(4,4) gauged linear sigma model describing Taub-NUT space. After dualizing the circle fiber, we find that the smeared NS5-brane target space metric receives corrections from multi-worldsheet instantons. These instantons are identified as Nielsen-Olesen vortices. We show that their effect is to break the isometry of the target space, localizing the NS5-brane at a point. The contribution from the k-instanton sector is shown to be proportional to the weighted integral of the Euler form over the k-vortex moduli space. The duality also predicts the, previously unknown, asymptotic exponential decay coefficient of the BPS vortex solution.