Duality invariance and higher derivatives

We dimensionally reduce the spacetime action of bosonic string theory, and that of the bosonic sector of heterotic string theory after truncating the Yang-Mills gauge fields, on a d-dimensional torus including all higher-derivative corrections to first order in α^'. A systematic procedure is developed that brings this action into a minimal form in which all fields except the metric carry only first-order derivatives. This action is shown to be invariant under O(d,d,R) transformations that acquire α^'-corrections through a Green-Schwarz type mechanism. We prove that, up to a global prefactor, the first-order α^'-corrections are uniquely determined by O(d,d,R) invariance.