Global conformal blocks via Shadow formalism
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917559229480960 |
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| author | Belavin, Vladimir Cabezas, J. Ramos |
| author_facet | Belavin, Vladimir Cabezas, J. Ramos |
| contents | We study $\mathfrak{sl}_2$ and $\mathfrak{sl}_3$ global conformal blocks on a sphere and a torus, using the shadow formalism. These blocks arise in the context of Virasoro and $\mathcal{W}_3$ conformal field theories in the large central charge limit. In the $\mathfrak{sl}_2$ case, we demonstrate that the shadow formalism yields the known expressions in terms of conformal partial waves. Then, we extend this approach to the $\mathfrak{sl}_3$ case and show that it allows to build simple integral representations for $\mathfrak{sl}_3$ global blocks. We demonstrate this construction on two examples: the four-point block on the sphere and the one-point torus block. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_02580 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global conformal blocks via Shadow formalism Belavin, Vladimir Cabezas, J. Ramos High Energy Physics - Theory We study $\mathfrak{sl}_2$ and $\mathfrak{sl}_3$ global conformal blocks on a sphere and a torus, using the shadow formalism. These blocks arise in the context of Virasoro and $\mathcal{W}_3$ conformal field theories in the large central charge limit. In the $\mathfrak{sl}_2$ case, we demonstrate that the shadow formalism yields the known expressions in terms of conformal partial waves. Then, we extend this approach to the $\mathfrak{sl}_3$ case and show that it allows to build simple integral representations for $\mathfrak{sl}_3$ global blocks. We demonstrate this construction on two examples: the four-point block on the sphere and the one-point torus block. |
| title | Global conformal blocks via Shadow formalism |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2401.02580 |