T-duality and two-loop renormalization flows

Manifest T-duality covariance of the one-loop renormalization group hows is shown for a generic bosonic sigma model with an abelian isometry, by referring a set of previously derived consistency conditions to the tangent space of the target. For a restricted background, T-duality transformations are then studied at the next order, and the ensuing consistency conditions are found to be satisfied by the two-loop Weyl anomaly coefficients of the model. This represents an extremely nontrivial test of the covariance of renormalization group Bows under T-duality, and a stronger condition than T-duality invariance of the string background effective action. (C) 1997 Elsevier Science B.V. PACS: 11.10.Hi; 11.10.Kk; 11.25.-w; 11.25.Db.