On the Virasoro fusion kernel at $c=25$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913472724336640 |
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| author | Ribault, Sylvain Tsiares, Ioannis |
| author_facet | Ribault, Sylvain Tsiares, Ioannis |
| contents | We find a formula for the Virasoro fusion kernel at $c=25$, in terms of the connection coefficients of the Painlevé VI differential equation. Our formula agrees numerically with previously known integral representations of the kernel. The derivation of our formula relies on a duality $c\to 26-c$ that is obeyed by the shift equations for the fusion and modular kernels. We conjecture that for $c<1$ the fusion and modular kernels are not smooth functions, but distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_09334 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Virasoro fusion kernel at $c=25$ Ribault, Sylvain Tsiares, Ioannis High Energy Physics - Theory Mathematical Physics We find a formula for the Virasoro fusion kernel at $c=25$, in terms of the connection coefficients of the Painlevé VI differential equation. Our formula agrees numerically with previously known integral representations of the kernel. The derivation of our formula relies on a duality $c\to 26-c$ that is obeyed by the shift equations for the fusion and modular kernels. We conjecture that for $c<1$ the fusion and modular kernels are not smooth functions, but distributions. |
| title | On the Virasoro fusion kernel at $c=25$ |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2310.09334 |