Tachyon kinks on non BPS D-branes

TL;DR

This paper studies solitonic solutions of the tachyon effective action on non-BPS D-branes, showing conditions under which they resemble BPS branes and analyzing their stability and spectrum.

Contribution

It demonstrates how tachyon kink solutions approximate BPS branes under certain potential conditions and analyzes their stability and perturbation spectrum.

Findings

Regular finite energy solutions on a circle

Conditions on potential for kink solutions to resemble BPS branes

Stability analysis of the solitons and perturbation spectrum

Abstract

We consider solitonic solutions of the DBI tachyon effective action for a non-BPS brane. When wrapped on a circle, these solutions are regular and have a finite energy. We show that in the decompactified limit, these solitons give Sen's infinitely thin finite energy kink -- interpreted as a BPS brane -- provided that some conditions on the potential hold. In particular, if for large $T$ the potential is exponential, $V = e^{-T^a}$, then Sen's solution is only found for $a<1$. For power-law potentials $V = 1/T^b$, one must have $b>1$. If these conditions are not satisfied, we show that the lowest energy configuration is the unstable tachyon vacuum with no kinks. We examine the stability of the solitons and the spectrum of small perturbations.