Dilaton transformation under abelian and non-abelian T-duality in the path-integral approach

We present a convenient method for deriving the transformation of the dilat on under T-duality in the path-integral approach. Subtleties arising in per forming the integral over the gauge fields are carefully analysed using Pau li-Villars regularization, thereby clarifying existing ambiguities in the l iterature, The formalism can not only be applied to the abelian case, but, and this for the first time, to the non-abelian case as well. Furthermore, by choosing a particular gauge, we directly obtain the target-space covaria nt expression for the dual geometry in the abelian case. Finally it is show n that the conditions for gauging non-abelian isometries are weaker than th ose generally found in the literature. (C) 1999 Elsevier Science B.V. All r ights reserved.