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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2311.18530 |
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| _version_ | 1866929225141846016 |
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| author | Sakatani, Yuho Satoh, Yuji |
| author_facet | Sakatani, Yuho Satoh, Yuji |
| contents | 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 $\widehat{\mathfrak{su}}(2)$ 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 $\widehat{\mathfrak{su}}(2)$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_18530 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On quantum Poisson-Lie T-duality of WZNW models Sakatani, Yuho Satoh, Yuji High Energy Physics - Theory 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 $\widehat{\mathfrak{su}}(2)$ 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 $\widehat{\mathfrak{su}}(2)$, 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. |
| title | On quantum Poisson-Lie T-duality of WZNW models |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2311.18530 |