CANONICAL EQUIVALENCE OF NON-ISOMETRIC SIGMA-MODELS AND POISSON-LIE T-DUALITY

We prove that a transformation, conjectured in our previous work, betw een phase-space variables in sigma-models related by Poisson-Lie T-dua lity is indeed a canonical one. We do so by explicitly demonstrating t he invariance of the classical Poisson brackets. This is the first exa mple of a class of sigma-models with no isometries related by canonica l transformations. In addition we discuss generating functionals of ca nonical transformations in generally non-isometric, bosonic and supers ymmetric sigma-models and derive the complete set of conditions that d etermine them. We apply this general formalism to find the generating functional for Poisson-Lie T-duality. We also comment on the relevance of this work to D-brane physics and to quantum aspects of T-duality. (C) 1998 Elsevier Science B.V.