Dilaton deformations in closed string field theory

The dilaton theorem implies that the contribution to the dilaton potentialfrom cubic interactions of all levels must be cancelled by the elementaryquartic self-coupling of dilatons. We use this expectation to test the quarticstructure of closed string field theory and to study the rules for levelexpansion. We explain how to use the results of Moeller to compute quarticinteractions of states that, just like the dilaton, are neither primary norhave a simple ghost dependence. Our analysis of cancellations is made richer bydiscussing simultaneous dilaton and marginal deformations. We find evidence fortwo facts: as the level is increased quartic interactions become suppressed andclosed string field theory may be able to describe arbitrarily large dilatondeformations.Comment: 32 pages, 3 figures, LaTeX. v2: Two typos corrected in equation (3.15) and above eqution (2.19). A line added above equation (5.3). v3: a mistake in equation (3.20) correcte