Duality beyond the first loop

In this article we give a calculation of the two-loop σ-model corrections to the T-duality map in string theory. We use the effective action approach, and analyze two-loop corrections in a specific subtraction scheme. Focusing on backgrounds which have a single Abelian isometry, we find the explicit form for the O(α^') modifications of the lowest order duality transformations. Rather surprisingly, the manifest two-loop duality depends crucially on the torsion field. In contrast with the dilaton and metric fields, which are merely passive spectators, the torsion plays a more active role, because of the anomalous couplings to the gauge fields that arise via dimensional reduction. Our results support the interpretation of T duality as an expansion in the inverse string tension α^', and its order-by-order realization as a manifest symmetry of the full string theory.