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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.09765 |
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| _version_ | 1866908534723051520 |
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| author | Fortin, Jean-François Quintavalle, Lorenzo Skiba, Witold |
| author_facet | Fortin, Jean-François Quintavalle, Lorenzo Skiba, Witold |
| contents | We derive expressions for the Virasoro OPE and four-point conformal blocks on the sphere via the resolution of identity recently determined in [Phys. Rev. D 111, 085010 (2025), arXiv:2409.12224]. Even though the resolution of the identity depends on Virasoro singular vectors, our expression for the blocks does not depend on their precise form, but just on their well-known conformal weights. We verify that our expression is compatible with -- but differs from -- Zamolodchikov's $h$-recursion relation and we also examine the impact of various large central charge limits in our formula. A Mathematica notebook with a simple implementation of our expression for the Virasoro conformal blocks is provided as an ancillary file. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form Fortin, Jean-François Quintavalle, Lorenzo Skiba, Witold High Energy Physics - Theory Mathematical Physics We derive expressions for the Virasoro OPE and four-point conformal blocks on the sphere via the resolution of identity recently determined in [Phys. Rev. D 111, 085010 (2025), arXiv:2409.12224]. Even though the resolution of the identity depends on Virasoro singular vectors, our expression for the blocks does not depend on their precise form, but just on their well-known conformal weights. We verify that our expression is compatible with -- but differs from -- Zamolodchikov's $h$-recursion relation and we also examine the impact of various large central charge limits in our formula. A Mathematica notebook with a simple implementation of our expression for the Virasoro conformal blocks is provided as an ancillary file. |
| title | Virasoro OPE and Conformal Blocks from the Inverse Shapovalov Form |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2509.09765 |