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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.12017 |
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| _version_ | 1866912829989191680 |
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| author | Linshaw, Andrew R. Qi, Fei |
| author_facet | Linshaw, Andrew R. Qi, Fei |
| contents | In this paper, we prove that simple affine vertex operator algebras with positive integral levels admit only trivial first-order deformations. Therefore, the deformation rigidity conjecture of strongly rational vertex operator algebras holds for these cases. We also show that the same holds simple affine vertex operator algebra of $\mathfrak{sl}_2$ at the non-integral admissible level $-4/3$. Therefore, neither $C_2$-cofiniteness nor rationality is a necessary condition for deformation rigidity of VOAs. We conjecture that the same should hold for every simple affine VOA that does not coincide with the corresponding universal affine VOA. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12017 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deformation rigidity of some simple affine VOAs Linshaw, Andrew R. Qi, Fei Quantum Algebra High Energy Physics - Theory In this paper, we prove that simple affine vertex operator algebras with positive integral levels admit only trivial first-order deformations. Therefore, the deformation rigidity conjecture of strongly rational vertex operator algebras holds for these cases. We also show that the same holds simple affine vertex operator algebra of $\mathfrak{sl}_2$ at the non-integral admissible level $-4/3$. Therefore, neither $C_2$-cofiniteness nor rationality is a necessary condition for deformation rigidity of VOAs. We conjecture that the same should hold for every simple affine VOA that does not coincide with the corresponding universal affine VOA. |
| title | Deformation rigidity of some simple affine VOAs |
| topic | Quantum Algebra High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.12017 |