T-duality and α′-corrections

We construct an O(d,d) invariant universal formulation of the first-order alpha'-corrections of the string effective actions involving the dilaton, metric and two-form fields. Two free parameters interpolate between four-derivative terms that are even and odd with respect to a Z(2)-parity transformation that changes the sign of the two-form field. The Z(2)-symmetric model reproduces the closed bosonic string, and the heterotic string effective action is obtained through a Z(2)-parity-breaking choice of parameters. The theory is an extension of the generalized frame formulation of Double Field Theory, in which the gauge transformations are deformed by a first-order generalized Green-Schwarz transformation. This deformation defines a duality covariant gauge principle that requires and fixes the four-derivative terms. We discuss the O ( d, d) structure of the theory and the (non-)covariance of the required field redefinitions.