Dilaton Deformations in Closed String Field Theory
  The dilaton theorem implies that the contribution to the dilaton potential from cubic interactions of all levels must be cancelled by the elementary quartic self-coupling of dilatons. We use this expectation to test the quartic structure of closed string field theory and to study the rules for level expansion. We explain how to use the results of Moeller to compute quartic interactions of states that, just like the dilaton, are neither primary nor have a simple ghost dependence. Our analysis of cancellations is made richer by discussing simultaneous dilaton and marginal deformations. We find evidence for two facts: as the level is increased quartic interactions become suppressed and closed string field theory may be able to describe arbitrarily large dilaton deformations. 
Haitang Yang and Barton Zwiebach