发表机构
School of Physics and Shing-Tung Yau Center, Southeast University; College of Computer Science and Technology, Zhejiang University（东南大学物理学院与邵逸夫数学中心; 浙江大学计算机科学与技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过测地线镶嵌将全息PEE张量网络模型推广到史瓦西黑洞背景，实现贝肯斯坦-霍金熵、RT公式及ER=EPR，开辟了超越AdS/CFT的全息建模新路径。
AI 中文摘要
在真空反德西特（AdS）空间中，几何结构允许通过测地线网络进行完美镶嵌。这种镶嵌精确地表征了背景，并且可以在其上定义AdS/CFT的部分纠缠熵（PEE）张量网络玩具模型。迄今为止，尚不清楚这种构造能否扩展到真空AdS之外。在本文中，我们朝这个方向迈出了第一步。我们证明史瓦西黑洞的外部区域及其爱因斯坦-罗森桥被从边界发射的特定测地线气体完美镶嵌，因此克罗夫顿重建在这些区域成立。然后我们证明这种测地线镶嵌及其定义的克罗夫顿重建可以扩展到更一般的黎曼流形。这使我们能够在更一般的几何背景上构造全息对偶的PEE张量网络模型。对于史瓦西背景的PEE张量网络模型，我们可以具体实现贝肯斯坦-霍金熵、龙-高柳公式和ER=EPR提议。我们的方法为超越AdS/CFT的全息玩具模型开辟了新途径。
英文摘要
In vacuum anti-de Sitter (AdS) space, the geometry admits a perfect tessellation by a geodesic network. This tessellation characterizes the background exactly, and a partial entanglement entropy (PEE) tensor-network toy model of AdS/CFT can be defined on it. It has so far been unclear whether this construction can be extended beyond vacuum AdS. In this paper we take the first step in this direction. We show that the exterior region of the Schwarzschild black hole and its Einstein--Rosen bridge are perfectly tessellated by a specific geodesic gas emitted from the boundary, so that Crofton reconstruction holds in these regions. We then prove that such a geodesic tessellation and the Crofton reconstruction it defines extend to more generic Riemannian manifolds. This allows us to construct a PEE tensor-network model of holographic duality on more generic geometric backgrounds. In the case of the PEE tensor-network model for the Schwarzschild background, we can concretely realize the Bekenstein--Hawking entropy, the Ryu--Takayanagi formula and the ER=EPR proposal. Our approach opens a new route towards holographic toy models beyond AdS/CFT.
Comments33 pages, 4 figures; v2: references fixed
