标题： 将代数Ryu-Takayanagi公式添加到代数重构定理中 显示英文标题

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

摘要： 研究全息理论的巨大进展之一是可以通过量子纠错来解释全息性，这使得纠缠楔形重构、Jafferis-Lewkowycz-Maldacena-Suh 公式、径向交换性和 Ryu-Takayanagi 公式相等。 我们称这种等价性为重建定理，其通过代数语言的无限维推广被认为排除了 Ryu-Takayanagi 公式的代数版本。 然而，最近关于引力代数的发展表明，包含代数形式的 Ryu-Takayanagi 公式是合理的。 在本文中，我们证明了对于 I 型和 II 型因子的情形，这种包含成立，这些情形预计可以描述全息理论。 显示英文摘要

摘要： 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.