Orthosymplectic Feigin-Semikhatov duality
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866918306099757056 |
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| author | Fasquel, Justine Nakatsuka, Shigenori |
| author_facet | Fasquel, Justine Nakatsuka, Shigenori |
| contents | We study the representation theory of the subregular W-algebra $\mathcal{W}^k(\mathfrak{so}_{2n+1},f_{sub})$ of type B and the principal W-superalgebra $\mathcal{W}^\ell(\mathfrak{osp}_{2|2n})$, which are related by an orthosymplectic analogue of Feigin-Semikhatov duality in type A. We establish a block-wise equivalence of weight modules over the W-superalgebras by using the relative semi-infinite cohomology functor and spectral flow twists, which generalizes the result of Feigin-Semikhatov-Tipunin for the N=2 superconformal algebra. In particular, the correspondence of Wakimoto type free field representations is obtained. When the level of the subregular W-algebra is exceptional, we classify the simple modules over the simple quotients $\mathcal{W}_k(\mathfrak{so}_{2n+1},f_{sub})$ and $\mathcal{W}_\ell(\mathfrak{osp}_{2|2n})$ and derive the character formulae. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14574 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Orthosymplectic Feigin-Semikhatov duality Fasquel, Justine Nakatsuka, Shigenori Representation Theory Mathematical Physics Quantum Algebra 17B69 (Primary) 17B67 (Secondary) We study the representation theory of the subregular W-algebra $\mathcal{W}^k(\mathfrak{so}_{2n+1},f_{sub})$ of type B and the principal W-superalgebra $\mathcal{W}^\ell(\mathfrak{osp}_{2|2n})$, which are related by an orthosymplectic analogue of Feigin-Semikhatov duality in type A. We establish a block-wise equivalence of weight modules over the W-superalgebras by using the relative semi-infinite cohomology functor and spectral flow twists, which generalizes the result of Feigin-Semikhatov-Tipunin for the N=2 superconformal algebra. In particular, the correspondence of Wakimoto type free field representations is obtained. When the level of the subregular W-algebra is exceptional, we classify the simple modules over the simple quotients $\mathcal{W}_k(\mathfrak{so}_{2n+1},f_{sub})$ and $\mathcal{W}_\ell(\mathfrak{osp}_{2|2n})$ and derive the character formulae. |
| title | Orthosymplectic Feigin-Semikhatov duality |
| topic | Representation Theory Mathematical Physics Quantum Algebra 17B69 (Primary) 17B67 (Secondary) |
| url | https://arxiv.org/abs/2307.14574 |