Order α′2 terms in the gravitational sector of string effective actions with the inclusion of the dilaton field

Abstract We discuss field redefinition ambiguities in string effective actions at order α ′2 , in the parameterization which is most suitable for comparison with the string amplitudes and the σ -model parameterization. We find that, when the dilaton field is included, the effective action can be most simply described by seven terms, whose coefficients can be fixed from the string S -matrix. We derive relations among the coefficients that appear in each of the above mentioned parameterizations.