The Bisognano-Wichmann property for non-unitary Wightman conformal field theories
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910186260660224 |
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| author | Tener, James E. |
| author_facet | Tener, James E. |
| contents | The Bisognano-Wichmann and Haag duality properties for algebraic quantum field theories are often studied using the powerful tools of Tomita-Takesaki modular theory for nets of operator algebras. In this article, we study analogous properties of nets of algebras generated by smeared Wightman fields, for potentially non-unitary theories. In light of recent work constructing Wightman field theories for (non-unitary) Möbius vertex algebras, we obtain a broadly applicable non-unitary version of the Bisognano-Wichmann property. In this setting we do not have access to the traditional tools of Hilbert space functional analysis, like functional calculus. Instead, results analogous to those of Tomita-Takesaki theory are derived `by hand' from the Wightman axioms. As an application, we demonstrate Haag duality for nets of smeared Wightman fields. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_10625 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Bisognano-Wichmann property for non-unitary Wightman conformal field theories Tener, James E. Mathematical Physics Operator Algebras Quantum Algebra 81T40 17B69 The Bisognano-Wichmann and Haag duality properties for algebraic quantum field theories are often studied using the powerful tools of Tomita-Takesaki modular theory for nets of operator algebras. In this article, we study analogous properties of nets of algebras generated by smeared Wightman fields, for potentially non-unitary theories. In light of recent work constructing Wightman field theories for (non-unitary) Möbius vertex algebras, we obtain a broadly applicable non-unitary version of the Bisognano-Wichmann property. In this setting we do not have access to the traditional tools of Hilbert space functional analysis, like functional calculus. Instead, results analogous to those of Tomita-Takesaki theory are derived `by hand' from the Wightman axioms. As an application, we demonstrate Haag duality for nets of smeared Wightman fields. |
| title | The Bisognano-Wichmann property for non-unitary Wightman conformal field theories |
| topic | Mathematical Physics Operator Algebras Quantum Algebra 81T40 17B69 |
| url | https://arxiv.org/abs/2506.10625 |