On the interdependence of the structure of string effective actions at different orders in α'

We discuss the interplay between field redefinition ambiguities at orders α' and α'2 in the gravitational sector of closed string theory effective actions for the case of a non-constant dilaton field. We show that, as a consequence, apparently different effective actions for this sector existing in the literature are, in fact, equivalent and discuss the implications of our results for the conjectured relationship between σ-model β-functions and string equations of motion. (orig.)