Adding the algebraic Ryu-Takayanagi formula to the algebraic reconstruction theorem

Mingshuai Xu; Haocheng Zhong

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arXiv · 2411.06361

Adding the algebraic Ryu-Takayanagi formula to the algebraic reconstruction theorem

Mingshuai Xu·Haocheng Zhong

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Abstract

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.

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Mingshuai Xu, Haocheng Zhong. 2024-11-10. Adding the algebraic Ryu-Takayanagi formula to the algebraic reconstruction theorem. https://arxiv.org/abs/2411.06361

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