Closed string tachyon condensation revisited

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.