Abstract
We study Poisson-Lie T-duality of the Wess-Zumino-Novikov-Witten (WZNW) models which are obtained from a class of Drinfel’d doubles and its generalization. In this case, the resultant WZNW models are known to be classically self-dual under Poisson-Lie T-duality. We describe an explicit construction of the associated currents, and discuss the conformal invariance under this duality. In a concrete example of the SU(2) WZNW model, we find that the self-duality is represented as a chiral automorphism of the \( \hat{\mathfrak{su}} \)(2) affine Lie algebra, though the transformation of the currents is non-local and non-linear. This classical automorphism can be promoted to the quantum one through the parafermionic formulation of \( \hat{\mathfrak{su}} \)(2), which in turn induces an isomorphism of the WZNW model. We thus find a full quantum equivalence of the dual pair under Poisson-Lie T-duality. The isomorphism is represented by a sign-change of a chiral boson or the order-disorder duality of the parafermionic conformal field theory as in Abelian T-duality on tori or in the mirror symmetry of the Gepner model.
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Acknowledgments
We would like to thank Y. Koga for useful discussions. This work is supported in part by JSPS KAKENHI Grant Numbers JP22K03631 and JP23K03391.
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Sakatani, Y., Satoh, Y. On quantum Poisson-Lie T-duality of WZNW models. J. High Energ. Phys. 2024, 150 (2024). https://doi.org/10.1007/JHEP01(2024)150
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DOI: https://doi.org/10.1007/JHEP01(2024)150