论文标题
双曲线建筑物的全息张量网络
Holographic tensor networks from hyperbolic buildings
论文作者
论文摘要
我们介绍了一个基于双曲建筑物理论的全息张量网络的统一框架。潜在的二元性将批量空间与一个可以与球体同态的边界相关联，但也与更通用的空间（如Menge Sponge型分形）相关联。在这种一般环境中，我们为满足互补恢复的大型散装地区提供了精确的结构。对于这些地区，我们的网络遵守ryu-takayanagi公式。 ryu-takayanagi表面的区域受边界的Hausdorff尺寸控制，并始终概括整数尺寸中全息纠缠熵的行为，以对非直觉案例。我们的构造在所有维度上都恢复了快乐的代码，并概括了布鲁哈特的几何形状。它还提供了全息有条件期望的无限维网的例子，并为分形空间开辟了一条途径。
We introduce a unifying framework for the construction of holographic tensor networks, based on the theory of hyperbolic buildings. The underlying dualities relate a bulk space to a boundary which can be homeomorphic to a sphere, but also to more general spaces like a Menger sponge type fractal. In this general setting, we give a precise construction of a large family of bulk regions that satisfy complementary recovery. For these regions, our networks obey a Ryu--Takayanagi formula. The areas of Ryu--Takayanagi surfaces are controlled by the Hausdorff dimension of the boundary, and consistently generalize the behavior of holographic entanglement entropy in integer dimensions to the non-integer case. Our construction recovers HaPPY--like codes in all dimensions, and generalizes the geometry of Bruhat--Tits trees. It also provides examples of infinite-dimensional nets of holographic conditional expectations, and opens a path towards the study of conformal field theory and holography on fractal spaces.
