AI 中文总结
本文在AdS/CFT半经典 regime 中，基于体线性化引力与边界CFT的GNS希尔伯特空间等距嵌入映射，证明了JLMS条件，并利用模交叉积构造验证了HRT公式，完善了全息引力的相关理论。
AI 中文摘要
在AdS/CFT对应关系的半经典 regime 内，我们考虑这样的极限：体动力学场是满足纯AdS时空背景上线性化爱因斯坦方程的线性化度规微扰。AdS/CFT对应关系为我们提供了一个全息映射，它是体线性化引力的GNS希尔伯特空间（相对于AdS不变真空）到边界CFT的GNS希尔伯特空间（相对于闵可夫斯基不变真空）的等距嵌入映射。我们假设该映射将体AdS真空映射到边界CFT真空，且允许AdS-Rindler楔重构。随后利用该映射，我们证明：对于边界中给定的球型区域A，与A关联的因果楔代数中体态相对于AdS真空的相对熵，与代码子空间中A区域内CFT可观测量代数内对偶CFT态相对于CFT真空的相对熵相匹配，这就是著名的Jafferis-Lewkowycz-Maldacena-Suh（JLMS）条件。此外，对于与A关联的因果楔中对应扰动体几何的局域半经典相干激发，我们利用模交叉积构造严格证明：与A关联的修饰II型代数中对偶CFT态的熵的依赖态部分，满足真空扣除的Hubeney-Rangamani-Takayanagi（HRT）公式。
英文摘要
Within the semi-classical regime of AdS/CFT correspondence, we consider the limit where the bulk dynamical field is linearized metric perturbations satisfying linearized Einstein equations over background pure AdS spacetime. AdS/CFT correspondence gives us a holographic map, which is an isometric embedding map of the GNS Hilbert space of linearized gravity in the bulk (w.r.t. the AdS-invariant vacuum) to the GNS Hilbert space of CFT in the boundary (w.r.t. the Minkowski-invariant vacuum). We assume that the map takes AdS-vacuum in the bulk to CFT-vacuum in the boundary and that it allows AdS-Rindler wedge reconstruction. Then using this map, we show that for a given ball-shaped region in the boundary $A$, the relative entropy of a bulk state w.r.t. the AdS vacuum in the algebra of causal wedge associated to $A$ matches with the relative entropy of the dual CFT state w.r.t. the CFT vacuum in the algebra of CFT observables in $A$ in the code subspace, which is known as Jafferis-Lewkowycz-Maldacena-Suh (JLMS) condition. Furthermore, for localized semi-classical coherent excitations in the causal wedge associated to $A$ which corresponds to perturbed bulk geometry, we show rigorously using modular crossed product construction that the state-dependent part of entropy of the dual CFT state in the dressed Type-II algebra associated to $A$ satisfies vacuum subtracted Hubeney-Rangamani-Takayanagi (HRT) formula.
Comments31+epsilon pages. 3 figures. Comments are welcome
