On quantum T-duality in σ models

The problem of quantum equivalence between non-linear sigma models related by Abelian or non-Abelian T-duality is studied in perturbation theory. Using the anomalous Ward identity for Weyl symmetry we derive a relation between the Weyl anomaly coefficients of the original and dual theories. The analysis 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 Poisson-Lie T-duality involving the Drinfeld double based on SU(2). In both cases quantum T-duality is established at the one-loop level. (C) 1998 Elsevier Science B.V.