Double Field Theory and $\alpha'$ corrections: explicit examples

We construct several solutions of effective actions for string theories beyond the supergravity approximation utilizing the framework of the Double Field Theory (DFT). The DFT effective actions, which are well suited for accommodating abelian and non-abelian T dualities, are naturally written in terms of modified connections and curvatures with torsion. We construct the most general solutions with vanishing modified torsion, and such geometries don't receive quantum corrections. We also compute the leading $\alpha'$ corrections to several supergravity solutions, including a pair of geometries related by a non-abelian T duality.