Ambiguity in the effective action in string theories

We point out that there is an ambiguity in some of the coefficients in the ''low-energy'' effective action (EA) for the massless string modes (in particular, the coefficients of the R2μν- and R2-terms in the gravitational EA's are ambiguous). In the S-matrix approach this ambiguity is a consequence of an off-shell ambiguity in the subtraction of the massless exchanges (manifesting itself as a freedom of field redefinitions which leave the S-matrix invariant because of the equivalence theorem). In the world-sheet path integral approach the ambiguity is due to the freedom in the choice of a 2D renormalization scheme and a Weyl gauge. We also comment on the relation with the second-quantized string approach. (orig.)