  We consider condensation of nearly marginal matter tachyons in closed string
field theory and observe that upon restricting to a subspace of states not
containing the ghost dilaton, the on-shell value of the action is proportional
to the shift of the central charge of the matter CFT. This correspondence lets
us find a novel conformal perturbation theory formula for the next-to-leading
order shift of the central charge for a generic theory, which we test on
Zamolodchikov's flow between consecutive minimal models. Upon reintroduction of
the dilaton couplings, it is plausible to have a vanishing value of the
on-shell action.
