  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.
