Conformal blocks of Wess-Zumino-Witten model from its free-field representation
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911296014778368 |
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| author | Morozov, Alexei Sifat, Hasib |
| author_facet | Morozov, Alexei Sifat, Hasib |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_23132 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conformal blocks of Wess-Zumino-Witten model from its free-field representation Morozov, Alexei Sifat, Hasib High Energy Physics - Theory Mathematical Physics 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. |
| title | Conformal blocks of Wess-Zumino-Witten model from its free-field representation |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2511.23132 |