A perturbative analysis of tachyon condensation

TL;DR

This paper uses a perturbative approach and Padé approximants to analyze tachyon condensation in open bosonic string theory, showing the energy of the stable vacuum approaches the expected value as the level of approximation increases.

Contribution

It introduces a novel perturbative expansion combined with Padé approximants to accurately estimate the tachyon potential and vacuum energy at high truncation levels.

Findings

Padé approximants improve energy estimates for the stable vacuum.

Energy approaches -1 as the level of truncation increases.

Results are consistent with previous level-truncation studies.

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, Pad\'e 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.