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. The Poisson-Lie T-duality transformation maps each model onto itself but acts non-trivially on the space of classical solutions.
Nuclear Physics B
- Pub Date:
- February 1998
- High Energy Physics - Theory
- 15 pages, latex, submitted to Nucl Phys B., some comments and formulas on Poisson-Lie T-duality transformation added