Supercritical stability, transitions and (pseudo)tachyons

TL;DR

This paper investigates the stability of highly supercritical string backgrounds with a time-like linear dilaton, showing that their late-time stability is maintained despite negative mass squared modes, due to suppressed back-reaction from a decaying string coupling.

Contribution

It demonstrates that in supercritical string theories with a linear dilaton, late-time stability persists because the decaying string coupling suppresses back-reaction from instabilities and particle production.

Findings

Late-time stability of supercritical string backgrounds is confirmed.

Back-reaction from tachyonic modes is suppressed by the decaying string coupling.

Transitions between supercritical theories do not cause significant back-reaction.

Abstract

Highly supercritical strings (c much greater than 15) with a time-like linear dilaton provide a large class of solutions to string theory, in which closed string tachyon condensation is under control (and follows the worldsheet renormalization group flow). In this note we analyze the late-time stability of such backgrounds, including transitions between them. The large friction introduced by the rolling dilaton and the rapid decrease of the string coupling suppress the back-reaction of naive instabilities. In particular, although the graviton, dilaton, and other light fields have negative effective mass squared in the linear dilaton background, the decaying string coupling ensures that their condensation does not cause large back-reaction. Similarly, the copious particles produced in transitions between highly supercritical theories do not back-react significantly on the solution. We discuss these features also in a somewhat more general class of time-dependent backgrounds with stable late-time asymptotics.