Poisson-Lie T-duality and Complex Geometry in N=2 superconformal WZNW models

TL;DR

This paper explores Poisson-Lie T-duality in N=2 superconformal WZNW models, revealing that duality is governed by complexified groups with symplectic structures, and demonstrating the models' Poisson-Lie symmetries.

Contribution

It establishes the role of complex Heisenberg doubles in defining Poisson-Lie T-duality for N=2 superconformal WZNW models and proves their symmetry properties.

Findings

Poisson-Lie T-duality is governed by complexified groups with Semenov-Tian-Shansky forms.

Models admit Poisson-Lie symmetries under actions of isotropic complex subgroups.

Duality acts nontrivially on classical solutions, mapping models to themselves.

Abstract

Poisson-Lie T-duality in N=2 superconformal WZNW models on the real Lie groups is considered. It is shown that Poisson-Lie T-duality is governed by the complexifications of the corresponding real groups endowed with Semenov-Tian-Shansky symplectic forms, i.e. Heisenberg doubles. Complex Heisenberg doubles are used to define on the group manifolds of the N=2 superconformal WZNW models the natural actions of the isotropic complex subgroups forming the doubles. It is proved that with respect to these actions N=2 superconformal WZNW models admit Poisson-Lie symmetries. Poisson-Lie T-duality transformation maps each model into itself but acts nontrivialy on the space of classical solutions.