Geometrical Tachyon Kinks and NS5 Branes

TL;DR

This paper explores the dynamics of geometrical tachyons and brane configurations in NS5 ring backgrounds, revealing stable kink solutions, the influence of electric fields, and the end states of probe branes, with implications for string theory models.

Contribution

It introduces explicit stable kink solutions for geometrical tachyons in NS5 ring backgrounds and analyzes the effects of electric fields and compactification on brane dynamics.

Findings

Stable kink solutions described by a cosine potential.

Stable solutions only occur at zero or critical electric field.

Tachyonic matter trapped inside the ring as end state.

Abstract

We further investigate the $NS$5 ring background using the tachyon map. Mapping the radion fields to the rolling tachyon helps to explain the motion of a probe $Dp$-brane in this background. It turns out that the radion field becomes tachyonic when the brane is confined to one dimensional motion inside the ring. We find explicit solutions for the geometrical tachyon field that describe stable kink solutions which are similar to those of the open string tachyon. Interestingly in the case of the geometric tachyon, the dynamics is controlled by a cosine potential. In addition, we couple a constant electric field to the probe-brane, but find that the only stable kink solutions occur when there is zero electric field or a critical field value. We also investigate the behaviour of Non-BPS branes in this background, and find that the end state of any probe brane is that of tachyonic matter 'trapped' around the interior of the ring. We conclude by considering compactification of the ring solution in one of the transverse directions.