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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.06361 |
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| _version_ | 1866918162083086336 |
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| author | Xu, Mingshuai Zhong, Haocheng |
| author_facet | Xu, Mingshuai Zhong, Haocheng |
| contents | A huge progress in studying holographic theories is that holography can be interpreted via the quantum error correction, which makes equal the entanglement wedge reconstruction, the Jafferis-Lewkowycz-Maldacena-Suh formula, the radial commutativity and the Ryu-Takayanagi formula. We call the equivalence the reconstruction theorem, whose infinite-dimensional generalization via algebraic language was believed to exclude the algebraic version of the Ryu-Takayanagi formula. However, recent developments regarding gravitational algebras have shown that the inclusion of the algebraic Ryu-Takayanagi formula is plausible. In this letter, we prove that such inclusion holds for the cases of type I/II factors, which are expected to describe holographic theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06361 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adding the algebraic Ryu-Takayanagi formula to the algebraic reconstruction theorem Xu, Mingshuai Zhong, Haocheng High Energy Physics - Theory Mathematical Physics A huge progress in studying holographic theories is that holography can be interpreted via the quantum error correction, which makes equal the entanglement wedge reconstruction, the Jafferis-Lewkowycz-Maldacena-Suh formula, the radial commutativity and the Ryu-Takayanagi formula. We call the equivalence the reconstruction theorem, whose infinite-dimensional generalization via algebraic language was believed to exclude the algebraic version of the Ryu-Takayanagi formula. However, recent developments regarding gravitational algebras have shown that the inclusion of the algebraic Ryu-Takayanagi formula is plausible. In this letter, we prove that such inclusion holds for the cases of type I/II factors, which are expected to describe holographic theories. |
| title | Adding the algebraic Ryu-Takayanagi formula to the algebraic reconstruction theorem |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2411.06361 |