On Geometry of Non-Abelian Duality

Abstract

We consider several pictures connected with non-abelian duality in 2d quantum field theory. A discrete version leads to 3d coloured pictures of quantum groups, using a non-abelian version of Poincare duality. A continuous classical version (Poisson-Lie T-duality) have some simple mechanical analogs. Finally a connection between Poisson-Lie T-duality and Courant algebroids is presented, which conjecturaly gives a unified picture.