The quantum poisson-Lie T-duality and mirror symmetry
Abstract
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.
- Publication:
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Soviet Journal of Experimental and Theoretical Physics
- Pub Date:
- July 1999
- DOI:
- 10.1134/1.558947
- arXiv:
- arXiv:hep-th/9812048
- Bibcode:
- 1999JETP...89....5P
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 17 pages, LaTex, misprints and references corrected