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arXiv · 2511.23132

Conformal blocks of Wess-Zumino-Witten model from its free-field representation

Alexei Morozov·Hasib Sifat
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Abstract

A powerful approach to the celebrated Wess-Zumino-Witten (WZW) model is provided by its free-field realization. However, explicit calculations of conformal blocks are not described in the literature in full detail. We begin this study with the simplest cases of the $\hat{sl}(2)_k$ and $\hat{sl}(3)_k$ WZW models, with special emphasis on their global $sl(2)$ and $sl(3)$ symmetries of the resulting correlators, which are not explicit in this formalism. Also non-trivial is the verification of the Knizhnik-Zamolodchikov equations in the $\hat{sl}(3)_k$ case, where the answers take the form of double integrals over screening charge positions and do not look like ordinary hypergeometric functions.

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Alexei Morozov, Hasib Sifat. 2025-11-28. Conformal blocks of Wess-Zumino-Witten model from its free-field representation. https://doi.org/10.1007/jhep08(2026)111

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