Poisson-Lie T-duality and Complex Geometry in N=2 superconformal WZNW models
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.
Keywords
Cite
@article{arxiv.hep-th/9706199,
title = {Poisson-Lie T-duality and Complex Geometry in N=2 superconformal WZNW models},
author = {S. E. Parkhomenko},
journal= {arXiv preprint arXiv:hep-th/9706199},
year = {2009}
}
Comments
15 pages, latex, submitted to Nucl Phys B., some comments and formulas on Poisson-Lie T-duality transformation added