Dynamical Dimension Change in Supercritical String Theory

We study tree-level solutions to heterotic string theory in which the number of spacetime dimensions 10+n changes dynamically due to closed string tachyon condensation. Taking the large-n limit, we compute the amount by which the dilaton gradient changes during the condensation process. At leading order in n we find that the change in the invariant magnitude of the dilaton gradient compensates the change in spacelike central charge on the worldsheet, so that the total worldsheet central charges are equal at early and late times. This result supports our interpretation of the worldsheet theory as a CFT of critical central charge which describes a dynamical reduction in the total number of spacetime dimensions.