On quantum T-duality in sigma models

The problem of quantum equivalence between non-linear sigma models related by Abelian or non-Abelian T-duality is studied in perturbation theory. Usin g the anomalous Ward identity for Weyl symmetry we derive a relation betwee n the Weyl anomaly coefficients of the original and dual theories. The anal ysis is not restricted to conformally invariant backgrounds. The formalism is applied to the study of two examples. The first is a model based on SU(2 ) non-Abelian T-duality. The second represents a simple realization of Pois son-Lie T-duality involving the Drinfeld double based on SU(2). In both cas es quantum T-duality is established at the one-loop level. (C) 1998 Elsevie r Science B.V.