Non-unitary Wightman CFTs and non-unitary vertex algebras
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911078784434176 |
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| author | Carpi, Sebastiano Raymond, Christopher Tanimoto, Yoh Tener, James E. |
| author_facet | Carpi, Sebastiano Raymond, Christopher Tanimoto, Yoh Tener, James E. |
| contents | We give an equivalence of categories between: (i) Möbius vertex algebras which are equipped with a choice of generating family of quasiprimary vectors, and (ii) (not-necessarily-unitary) Möbius-covariant Wightman conformal field theories on the unit circle. We do not impose any technical restrictions on the theories considered (such as finite-dimensional conformal weight spaces or simplicity), yielding the most general equivalence between these two axiomatizations of two-dimensional chiral conformal field theory. This provides new opportunities to study non-unitary vertex algebras using the lens of algebraic conformal field theory and operator algebras, which we demonstrate by establishing a non-unitary version of the Reeh-Schlieder theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08454 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-unitary Wightman CFTs and non-unitary vertex algebras Carpi, Sebastiano Raymond, Christopher Tanimoto, Yoh Tener, James E. Mathematical Physics Quantum Algebra 81T40, 17B69, 81T05 We give an equivalence of categories between: (i) Möbius vertex algebras which are equipped with a choice of generating family of quasiprimary vectors, and (ii) (not-necessarily-unitary) Möbius-covariant Wightman conformal field theories on the unit circle. We do not impose any technical restrictions on the theories considered (such as finite-dimensional conformal weight spaces or simplicity), yielding the most general equivalence between these two axiomatizations of two-dimensional chiral conformal field theory. This provides new opportunities to study non-unitary vertex algebras using the lens of algebraic conformal field theory and operator algebras, which we demonstrate by establishing a non-unitary version of the Reeh-Schlieder theorem. |
| title | Non-unitary Wightman CFTs and non-unitary vertex algebras |
| topic | Mathematical Physics Quantum Algebra 81T40, 17B69, 81T05 |
| url | https://arxiv.org/abs/2409.08454 |