EQUIVALENCE OF THE STRING EQUATIONS OF MOTION AND THE SIGMA-MODEL WEYL-INVARIANCE CONDITIONS AT ORDER ALPHA'2 - DEPENDENCE ON THE DILATON FIELD

We study the structure of effective actions of closed-string theory at order alpha'2, when the dilaton field is included. We show, in particular, that the way field-redefinition ambiguities are fixed at order alpha' affects the order-alpha'2 results, and find that, as a consequence, different forms for the effective action existing in the literature are in fact equivalent. We discuss the implications of our results for the conjectured relationship between string equations of motion and sigma-model beta-functions.