Poisson-Lie T-duality and N=2 superconformal WZNW models on compact groups

TL;DR

This paper explores the supersymmetric extension of Poisson-Lie T-duality in N=2 superconformal WZNW models on compact groups, highlighting the role of Drinfeld's doubles and demonstrating duality properties in specific models.

Contribution

It introduces a supersymmetric generalization of Poisson-Lie T-duality for N=2 superconformal WZNW models on compact groups, utilizing complexified doubles.

Findings

Poisson-Lie T-duality maps the U(2)-WZNW model onto itself with nontrivial effects.

The complexification of compact groups forms the Drinfeld's doubles used in the duality.

Supersymmetric generalization extends duality concepts to higher-dimensional models.

Abstract

The supersymmetric generalization of Pisson-Lie T-duality in 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 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 nontrivialy 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.