Non-Abelian duality in the string effective action

We study the symmetry of the one-loop effective action of bosonic string th eory under non-Abelian T-duality transformations. It is shown that the orig inal Lagrangian and its dual are proportional. This result implies that the corresponding reduced low energy effective actions are equivalent and lead s to a functional relation between the Weyl anomaly coefficients of the ori ginal and dual two-dimensional non-linear sigma models. Finally, we apply t his Formalism to some simple examples. (C) 2001 Elsevier Science B.V. All r ights reserved.