Four-derivative couplings via the T-duality invariance constraint

We examine the proposal that the dimensional reduction of the effective action of perturbative string theory on a circle should be invariant under T-duality transformations. The T-duality transformations are the standard Buscher rules plus some higher covariant derivatives. By explicit calculations at order alpha' for metric, dilaton, and B-field, we show that the T-duality constraint can fix both the effective action and the higher derivative corrections to the Buscher rules up to an overall factor. The corrections depend on the scheme that one uses for the effective action. We have found the effective action and its corresponding T-duality transformations in an arbitrary scheme.