Conformal nets from minimal W-algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909879119118336 |
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| author | Carpi, Sebastiano Gaudio, Tiziano |
| author_facet | Carpi, Sebastiano Gaudio, Tiziano |
| contents | We show the strong graded locality of all unitary minimal W-algebras, so that they give rise to irreducible graded-local conformal nets. Among these unitary vertex superalgebras, up to taking tensor products with free fermion vertex superalgebras, there are the unitary Virasoro vertex algebras (N=0) and the unitary N=1,2,3,4 super-Virasoro vertex superalgebras. Accordingly, we have a uniform construction that gives, besides the already known N=0,1,2 super-Virasoro nets, also the new N=3,4 super-Virasoro nets. All strongly rational unitary minimal W-algebras give rise to previously known completely rational graded-local conformal nets and we conjecture that the converse is also true. We prove this conjecture for all unitary W-algebras corresponding to the N=0,1,2,3,4 super-Virasoro vertex superalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04270 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conformal nets from minimal W-algebras Carpi, Sebastiano Gaudio, Tiziano Mathematical Physics High Energy Physics - Theory Operator Algebras Quantum Algebra We show the strong graded locality of all unitary minimal W-algebras, so that they give rise to irreducible graded-local conformal nets. Among these unitary vertex superalgebras, up to taking tensor products with free fermion vertex superalgebras, there are the unitary Virasoro vertex algebras (N=0) and the unitary N=1,2,3,4 super-Virasoro vertex superalgebras. Accordingly, we have a uniform construction that gives, besides the already known N=0,1,2 super-Virasoro nets, also the new N=3,4 super-Virasoro nets. All strongly rational unitary minimal W-algebras give rise to previously known completely rational graded-local conformal nets and we conjecture that the converse is also true. We prove this conjecture for all unitary W-algebras corresponding to the N=0,1,2,3,4 super-Virasoro vertex superalgebras. |
| title | Conformal nets from minimal W-algebras |
| topic | Mathematical Physics High Energy Physics - Theory Operator Algebras Quantum Algebra |
| url | https://arxiv.org/abs/2506.04270 |