CFT缝纫作为AdS剪切和粘贴的双重功能
CFT sewing as the dual of AdS cut-and-paste
摘要：
CPT映射允许量子场论的两个态在CPT共轭的部分柯西曲面$R_1,R_2$上缝合在一起，从而在一个新的时空上形成一个态。我们研究了这种操作的全息对偶的情况下，其中的原始状态是CPT共轭内$R_1,R_2$领先的顺序，在体牛顿常数$G$，和其中的体量子数占主导地位的经典体几何$g_1,g_2$。对于在$R_1,R_2$ HRT-表面上的固定区域的状态，我们认为，通过从$g_1,g_2$中删除$R_1,R_2$的纠缠楔，将${\bar R}_1, {\bar R}_2$的剩余互补纠缠楔粘在一起，并求解过去和未来的运动方程，给出了与新缝合状态对偶的体几何$g_1 \# g_2$。该论证使用体积路径积分，并假设它由某个自然鞍控制。对于HRT区域不固定的状态，同样的批量剪切和粘贴是双重的修改缝合，产生了Dutta和Faulkner最近讨论的规范纯化状态$\sqrtρ$的泛化。任何一种形式的构造都可以用来构建与多体反射熵相关的体几何对偶的CFT态。
英文摘要：
The CPT map allows two states of a quantum field theory to be sewn together over CPT-conjugate partial Cauchy surfaces $R_1,R_2$ to make a state on a new spacetime. We study the holographic dual of this operation in the case where the original states are CPT-conjugate within $R_1,R_2$ to leading order in the bulk Newton constant $G$, and where the bulk duals are dominated by classical bulk geometries $g_1,g_2$. For states of fixed area on the $R_1,R_2$ HRT-surfaces, we argue that the bulk geometry $g_1 \# g_2$ dual to the newly sewn state is given by deleting the entanglement wedges of $R_1,R_2$ from $g_1,g_2$, gluing the remaining complementary entanglement wedges of ${\bar R}_1, {\bar R}_2$ together across the HRT surface, and solving the equations of motion to the past and future. The argument uses the bulk path integral and assumes it to be dominated by a certain natural saddle. For states where the HRT area is not fixed, the same bulk cut-and-paste is dual to a modified sewing that produces a generalization of the canonical purification state $\sqrtρ$ discussed recently by Dutta and Faulkner. Either form of the construction can be used to build CFT states dual to bulk geometries associated with multipartite reflected entropy.
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