Canonical equivalence of non-isometric σ-models and Poisson-Lie T-duality Original Research Article

We prove that a transformation, conjectured in our previous work, between phase-space variables in σ-models related by Poisson-Lie T-duality is indeed a canonical one. We do so by explicitly demonstrating the invariance of the classical Poisson brackets. This is the first example of a class of σ-models with no isometries related by canonical transformations. In addition we discuss generating functionals of canonical transformations in generally non-isometric, bosonic and supersymmetric σ-models and derive the complete set of conditions that determine 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.