Poisson–Lie T-Duality and N=2 Superconformal WZNW Models on Compact Groups

Abstract

The supersymmetric generalization of Poisson–Lie T-duality in the N=2 superconformal WZNW models on the compact groups is considered. It is shown that the role of Drinfeld's doubles play the complexifications of the corresponding compact groups. These complex doubles are used to define the natural actions of the isotropic subgroups forming the doubles on the group manifolds of the N=2 superconformal WZNW models. The Poisson–Lie T-duality in N=2 superconformal U(2)-WZNW model is considered in details. It is shown that this model admits Poisson–Lie symmetries with respect to the isotropic subgroups forming Drinfeld's double Gl (2,C). Poisson–Lie T-duality transformation maps this model into itself but acts nontrivially on the space of classical solutions. Supersymmetric generalization of Poisson–Lie T-duality in N=2 superconformal WZNW models on the compact groups of higher dimensions is proposed.