A perturbative analysis of tachyon condensation

TL;DR

This work tackles tachyon condensation in open bosonic string theory by perturbing around the unstable D25-brane vacuum and using Padé resummation to access the nonperturbative vacuum energy. It computes the effective tachyon potential $V(\phi)=\sum_{n=2}^{\infty} c_n (\kappa g)^{n-2} \phi^n$ from level-truncated data, then extrapolates coefficients with $1/L$ corrections and constructs Padé approximants to predict the vacuum energy at high levels. The approach reproduces known level-truncation results and explains overshoot phenomena, finding that the energy can dip below $-E_0$ but ultimately approaches $-1$ from below as the truncation level grows, in agreement with recent numerical results. Overall, the perturbative-Padé framework provides a robust, gauge-fixed cross-check of nonperturbative open-string vacuum physics consistent with Sen's conjectures and Gaiotto–Rastelli findings.

Abstract

Tachyon condensation in the open bosonic string is analyzed using a perturbative expansion of the tachyon potential around the unstable D25-brane vacuum. Using the leading terms in the tachyon potential, Padé approximants can apparently give the energy of the stable vacuum to arbitrarily good accuracy. Level-truncation approximations up to level 10 for the coefficients in the tachyon potential are extrapolated to higher levels and used to find approximants for the full potential. At level 14 and above, the resulting approximants give an energy less than -1 in units of the D25-brane tension, in agreement with recent level-truncation results by Gaiotto and Rastelli. The extrapolated energy continues to decrease below -1 until reaching a minimum near level 26, after which the energy turns around and begins to approach -1 from below. Within the accuracy of this method, these results are completely consistent with an energy which approaches -1 as the level of truncation is taken to be arbitrarily large.