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The quantum poisson-Lie T-duality and mirror symmetry

  • Nuclei, Particles, and Their Interaction
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Abstract

Poisson-Lie T-duality in quantum N=2 superconformal Wess-Zumino-Novikov-Witten 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 transformation is given by an automorphism which interchanges the isotropic subalgebras of the underlying Manin triple in one of the chirality sectors of the model. It is shown that quantum Poisson-Lie T-duality acts on the N=2 super-Virasoro algebra generators of the quantum models as a mirror symmetry acts: in one of the chirality sectors it is a 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 quantum 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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Authors and Affiliations

  1. Landau Institute for Theoretical Physics, 142432, Chernogolovka, Moscow Region, Russia

    S. E. Parkhomenko

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Zh. Éksp. Teor. Fiz. 116, 11–25 (July 1999)

Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.

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Parkhomenko, S.E. The quantum poisson-Lie T-duality and mirror symmetry. J. Exp. Theor. Phys. 89, 5–12 (1999). https://doi.org/10.1134/1.558947

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  • DOI: https://doi.org/10.1134/1.558947

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