Quantum Correction to Generalized T Dualities

Poisson-Lie duality is a generalization of Abelian and non-Abelian T duality, and it can be viewed as a map between solutions of the low-energy effective equations of string theory, i.e., at the (super) gravity level. We show that this fact extends to the next order in α^{'} (two loops in σ-model perturbation theory) provided that the map is corrected. The α^{'} correction to the map is induced by the anomalous Lorentz transformations of the fields that are necessary to go from a doubled O(D,D)-covariant formulation to the usual (super)gravity description.