Minimal W-algebras of $\mathfrak{so}_N$ at level minus one
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915350207004672 |
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| author | Creutzig, Thomas Fasquel, Justine Kovalchuk, Vladimir Linshaw, Andrew R. Nakatsuka, Shigenori |
| author_facet | Creutzig, Thomas Fasquel, Justine Kovalchuk, Vladimir Linshaw, Andrew R. Nakatsuka, Shigenori |
| contents | For $N \in\mathbb Z_{\geq 7}$ we show that the simple minimal $\mathcal{W}$-algebra of $\mathfrak{so}_N$ at level minus one is isomorphic to the even subalgebra of the tensor product of the simple affine vertex superalgebra of $\mathfrak{osp}_{1|2}$ at level $\frac{N-6}{2}$ with $N-4$ free fermions. In particular when $N$ is even this minimal $\mathcal{W}$-algebra is strongly rational as conjectured by Arakawa-Moreau. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15605 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal W-algebras of $\mathfrak{so}_N$ at level minus one Creutzig, Thomas Fasquel, Justine Kovalchuk, Vladimir Linshaw, Andrew R. Nakatsuka, Shigenori Representation Theory Quantum Algebra For $N \in\mathbb Z_{\geq 7}$ we show that the simple minimal $\mathcal{W}$-algebra of $\mathfrak{so}_N$ at level minus one is isomorphic to the even subalgebra of the tensor product of the simple affine vertex superalgebra of $\mathfrak{osp}_{1|2}$ at level $\frac{N-6}{2}$ with $N-4$ free fermions. In particular when $N$ is even this minimal $\mathcal{W}$-algebra is strongly rational as conjectured by Arakawa-Moreau. |
| title | Minimal W-algebras of $\mathfrak{so}_N$ at level minus one |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2506.15605 |