发表机构
University of British Columbia（不列颠哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在AdS$_3$中证明广义纠缠楔由纠缠楔的并集与交集构成，并利用Crofton公式将其周长表示为测地线测度，从而将GWs的强次可加性归结为边界CFT熵的强次可加性，表明GWs对应更一般的CFT子系统。
AI 中文摘要
广义纠缠楔（GWs）由Bousso和Penington针对一般时空中引力区域提出，其具有普通纠缠楔的许多性质，包括嵌套性、单调性及其广义熵的强次可加性。在AdS/CFT中，纠缠楔的相应性质是共形场论（CFT）对偶结构的结果。本文探讨GWs的性质是否具有类似起源。我们在真空AdS$_3$中，在$G$的领头阶下研究此问题。我们首先证明静态切片上的每个GW都是测地凸区域的并集。每个这样的区域是普通纠缠楔的交集，因此每个GW由纠缠楔的并集和交集构成。然后我们利用积分几何的Crofton公式，将凸区域的周长写为与其相交的测地线集合的测度。在AdS$_3$中，每条测地线都是边界区间的Ryu-Takayanagi曲面，因此该测度可以用CFT区间的von Neumann熵表示。CFT熵的强次可加性保证了测度的正性。GWs的单调性和强次可加性随后由测地线集合之间的简单不等式得出。因此，GWs的强次可加性是边界上强次可加性的直接结果。我们的结果进一步表明，GWs对应于比边界子区域更一般的CFT子系统。
英文摘要
Generalized entanglement wedges (GWs), proposed by Bousso and Penington for gravitating regions in general spacetimes, share many properties of ordinary entanglement wedges, including nesting, monotonicity and strong subadditivity of their generalized entropies. In AdS/CFT, the corresponding properties of entanglement wedges are consequences of the structure of the dual CFT. In this paper we ask whether the properties of GWs have a similar origin. We explore this question in vacuum AdS$_3$ at leading order in $G$. We first show that every GW on a static slice is a union of geodesically convex regions. Each such region is an intersection of ordinary entanglement wedges, so every GW is built from unions and intersections of entanglement wedges. We then use the Crofton formula of integral geometry to write the perimeter of a convex region as the measure of the set of geodesics that intersect it. In AdS$_3$ every geodesic is the Ryu--Takayanagi surface of a boundary interval, so this measure can be written in terms of the von Neumann entropies of CFT intervals. Strong subadditivity of the CFT entropy guarantees that the measure is positive. Monotonicity and strong subadditivity of GWs then follow from simple inequalities between sets of geodesics. The strong subadditivity of GWs is therefore a direct consequence of strong subadditivity on the boundary. Our results further suggest that GWs correspond to subsystems of the CFT that are more general than boundary subregions.
Comments11 pages, 3 figures
