Supercritical stability, transitions, and (pseudo)tachyons

Highly supercritical strings (c much greater than 15) with a time-like lineardilaton provide a large class of solutions to string theory, in which closedstring tachyon condensation is under control (and follows the worldsheetrenormalization group flow). In this note we analyze the late-time stability ofsuch backgrounds, including transitions between them. The large frictionintroduced by the rolling dilaton and the rapid decrease of the string couplingsuppress the back-reaction of naive instabilities. In particular, although thegraviton, dilaton, and other light fields have negative effective mass squaredin the linear dilaton background, the decaying string coupling ensures thattheir condensation does not cause large back-reaction. Similarly, the copiousparticles produced in transitions between highly supercritical theories do notback-react significantly on the solution. We discuss these features also in asomewhat more general class of time-dependent backgrounds with stable late-timeasymptotics.Comment: 21 pages, harvmac. v2: added referenc