  Manifest T-duality covariance of the one-loop renormalization group flows 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 non-trivial test of the covariance of renormalization
group flows under T-duality, and a stronger condition than T-duality invariance
of the string background effective action.
