POISSON-LIE T-DUALITY BEYOND THE CLASSICAL LEVEL AND THE RENORMALIZATION-GROUP

In order to study quantum aspects of sigma-models related by Poisson-L ie T-duality, we construct three- and two-dimensional models that corr espond, in one of the dual faces, to deformations of S-3 and S-2. Thei r classical canonical equivalence is demonstrated by means of a genera ting functional, which we explicitly compute. We examine how they beha ve under the renormalization group and show that dually related models have the same 1-loop beta functions for the coupling and deformation parameters. We find non-trivial fixed points in the ultraviolet, where the theories do not become asymptotically free. This suggests that th e limit of Poisson-Lie T-duality to the usual Abelian and non-Abelian T-dualities does not exist quantum mechanically, although it does so c lassically. (C) 1998 Elsevier Science B.V. All rights reserved.