Supercritical stability, transitions, and (pseudo)tachyons

Highly supercritical strings ($c\ensuremath{\gg}15$) with a timelike linear dilaton provide a large class of solutions to string theory, in which closed string tachyon condensation is under control (and follows the world sheet 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 backreaction 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 backreaction. 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.