On the Quantum Poisson-Lie T-duality and Mirror Symmetry

Details On the Quantum Poisson-Lie T-duality and Mirror Symmetry On the Quantum Poisson-Lie T-duality and Mirror Symmetry

1998-12-05

arxiv.org/abs/hep-th/9812048v4

J.Exp.Theor.Phys. 89 (1999) 5-12; Zh.Eksp.Teor.Fiz. 116 (1999) 11-25

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, LaTex, misprints and references corrected

Scientific paper

10.1134/1.558947

Poisson-Lie T-duality in quantum N=2 superconformal WZNW models is considered. The Poisson-Lie T-duality transformation rules of the super-Kac-Moody algebra currents are found from the conjecture that, as in the classical case, the quantum Poisson-Lie T-duality is given by an automorphism which interchanges the isotropic subalgebras of the underlying Manin triple of the model. It is shown that quantum Poisson-Lie T-duality acts on the generators of the N=2 super-Virasoro algebra of the quantum models as a mirror symmetry acts: in one of the chirality sectors it is trivial transformation while in another chirality sector it changes the sign of the U(1) current and interchanges the spin-3/2 currents. A generalization of Poisson-Lie T-duality for the Kazama-Suzuki models is proposed. It is shown that quantum Poisson-Lie T-duality acts in these models as a mirror symmetry also.

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