Modular invariance of characters of quasi-lisse vertex algebras
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917543893008384 |
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| author | Arakawa, Tomoyuki van Ekeren, Jethro Li, Hao |
| author_facet | Arakawa, Tomoyuki van Ekeren, Jethro Li, Hao |
| contents | We study spaces of conformal blocks associated with line bundles over elliptic curves, with coefficients in a vertex algebra. For vertex algebras satisfying suitable finiteness and semisimplicity conditions, which are met by all admissible affine vertex algebras as well as admissible W-algebras associated with nilpotent elements of standard Levi type, we prove the holonomicity of the sheaf of conformal blocks over the moduli space of bundles. Furthermore, we show that the space of flat sections of the associated Jacobi-invariant connection is spanned by trace functions on modules. This result provides a substantial generalization of the celebrated theorem of Yongchang Zhu to quasi-lisse vertex algebras. As a special case, we deduce that for affine vertex algebras at admissible level, the dimension of the space of conformal blocks coincides with the number of admissible weights at that level. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_29921 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Modular invariance of characters of quasi-lisse vertex algebras Arakawa, Tomoyuki van Ekeren, Jethro Li, Hao Quantum Algebra High Energy Physics - Theory Mathematical Physics Representation Theory 17B67, 17B69, 81R10 We study spaces of conformal blocks associated with line bundles over elliptic curves, with coefficients in a vertex algebra. For vertex algebras satisfying suitable finiteness and semisimplicity conditions, which are met by all admissible affine vertex algebras as well as admissible W-algebras associated with nilpotent elements of standard Levi type, we prove the holonomicity of the sheaf of conformal blocks over the moduli space of bundles. Furthermore, we show that the space of flat sections of the associated Jacobi-invariant connection is spanned by trace functions on modules. This result provides a substantial generalization of the celebrated theorem of Yongchang Zhu to quasi-lisse vertex algebras. As a special case, we deduce that for affine vertex algebras at admissible level, the dimension of the space of conformal blocks coincides with the number of admissible weights at that level. |
| title | Modular invariance of characters of quasi-lisse vertex algebras |
| topic | Quantum Algebra High Energy Physics - Theory Mathematical Physics Representation Theory 17B67, 17B69, 81R10 |
| url | https://arxiv.org/abs/2605.29921 |