Spectral flow and application to unitarity of representations of minimal $W$-algebras
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910106275282944 |
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| author | Kac, Victor G. Frajria, Pierluigi Möseneder Papi, Paolo |
| author_facet | Kac, Victor G. Frajria, Pierluigi Möseneder Papi, Paolo |
| contents | Using spectral flow, we provide a proof of [11, Theorem 9.17] on unitarity of Ramond twisted non-extremal representations of unitary minimal $W$-algebras that does not rely on the still conjectural exactness of the twisted quantum reduction functor (see Conjecture 9.11 of [11]). When $\mathfrak g = spo(2|2n)$, $F (4$), $D(2, 1; \frac{m}{n})$, it is also proven that the unitarity of extremal (=massless) representations of the unitary minimal $W$-algebra $W^k_{\min}(\mathfrak g)$ in the Ramond sector is equivalent to the unitarity of extremal representations in the Neveu-Schwarz sector. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06873 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral flow and application to unitarity of representations of minimal $W$-algebras Kac, Victor G. Frajria, Pierluigi Möseneder Papi, Paolo Representation Theory Mathematical Physics Using spectral flow, we provide a proof of [11, Theorem 9.17] on unitarity of Ramond twisted non-extremal representations of unitary minimal $W$-algebras that does not rely on the still conjectural exactness of the twisted quantum reduction functor (see Conjecture 9.11 of [11]). When $\mathfrak g = spo(2|2n)$, $F (4$), $D(2, 1; \frac{m}{n})$, it is also proven that the unitarity of extremal (=massless) representations of the unitary minimal $W$-algebra $W^k_{\min}(\mathfrak g)$ in the Ramond sector is equivalent to the unitarity of extremal representations in the Neveu-Schwarz sector. |
| title | Spectral flow and application to unitarity of representations of minimal $W$-algebras |
| topic | Representation Theory Mathematical Physics |
| url | https://arxiv.org/abs/2508.06873 |