The Virasoro Completeness Relation and Inverse Shapovalov Form
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913786979418112 |
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| author | Fortin, Jean-François Quintavalle, Lorenzo Skiba, Witold |
| author_facet | Fortin, Jean-François Quintavalle, Lorenzo Skiba, Witold |
| contents | In this work, we introduce an explicit expression for the inverse of the symmetric bilinear form of Virasoro Verma modules, the so-called Shapovalov form, in terms of singular vector operators and their conformal dimensions. Our proposed expression also determines the resolution of the identity for Verma modules of the Virasoro algebra, and can be thus employed in the computation of Virasoro conformal blocks via the sewing procedure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12224 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Virasoro Completeness Relation and Inverse Shapovalov Form Fortin, Jean-François Quintavalle, Lorenzo Skiba, Witold High Energy Physics - Theory Mathematical Physics In this work, we introduce an explicit expression for the inverse of the symmetric bilinear form of Virasoro Verma modules, the so-called Shapovalov form, in terms of singular vector operators and their conformal dimensions. Our proposed expression also determines the resolution of the identity for Verma modules of the Virasoro algebra, and can be thus employed in the computation of Virasoro conformal blocks via the sewing procedure. |
| title | The Virasoro Completeness Relation and Inverse Shapovalov Form |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2409.12224 |