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
该研究在全息张量网络玩具模型中验证了广义纠缠楔与半经典极限下可观测量子代数相关联的假设，证明了每个区域存在典范子代数，并探讨了代数运算与几何运算的对应关系，以及熵的单调性和强次可加性，最后构造了类型II_1冯·诺依曼代数以精确关联广义纠缠楔区域。
AI 中文摘要
在先前的工作2511.21852中，我们探讨了在一般量子引力理论中，被称为广义纠缠楔（由Bousso和Penington引入）的时空区域在半经典极限下具有相关联的可观测量子代数的假设。我们定义了与这些子代数相关的熵，该熵满足与广义纠缠楔的广义引力熵相同的单调性和强次可加性性质。在此，我们利用全息张量网络玩具模型来检验这些思想的各个方面。在此背景下，广义纠缠楔的类比是这样一个区域：任何包含它的区域都没有更少的边界腿数。在大键维极限（类似于半经典极限）下，我们认为每个这样的区域在边界希尔伯特空间上的完整可观测量代数中具有一个典范关联的子代数，以及一族酉相关的冯·诺依曼因子子代数。我们详细研究了这些子代数上的各种代数运算（例如它们的交集、并集和交换子）如何与张量网络区域上的相应几何运算相关联。我们研究了广义纠缠楔的广义熵的单调性和强次可加性性质在多大程度上源于我们代数熵的性质。我们还引入了一个与子代数$\mathcal{A}$相关的替代熵量$S(\omega || \omega \circ E_{\mathcal{A}'})$，该量在适当条件下也满足单调性和强次可加性性质。最后，我们解释了如何基于具有递增键维的无限随机张量网络族来定义类型$II_1$冯·诺依曼代数，使得与广义纠缠楔对应的区域可以与该完整代数的精确子代数相关联。
英文摘要
In a previous work 2511.21852, we explored the hypothesis that in general theories of quantum gravity, spacetime regions known as generalized entanglement wedges (introduced by Bousso and Penington) have an associated subalgebra of observables in a semiclassical limit. We defined an entropy associated with these subalgebras that obeys the same monotonicity and strong subadditivity properties as the generalized gravitational entropy of generalized entanglement wedges. Here, we test aspects of these ideas making use of tensor network toy models for holography. In this context, the analog of a generalized entanglement wedge is a region for which no region containing it has a smaller number of boundary legs. In the limit of large bond dimension (analogous to the semiclassical limit), we argue that each such region has a canonically associated subalgebra of the full algebra of observables on the boundary Hilbert space, as well as a family of unitarily related von Neumann factor subalgebras. We investigate in detail how various algebraic operations on these subalgebras (e.g. their intersections, joins, and commutants) are related to corresponding geometrical operations on the tensor network regions. We study to what extent the monotonicity and strong subadditivity properties of generalized entropy for generalized entanglement wedges follow from properties of our algebraic entropy. We also introduce an alternative entropic quantity $S(ω|| ω\circ E_{\mathcal{A}'})$ associated with a subalgebra $\mathcal{A}$ that also obeys monotonicity and strong subadditivity properties with suitable conditions. Finally, we explain how to define a type $II_1$ von Neumann algebra based on an infinite family of random tensor networks with increasing bond dimension such that the regions corresponding to generalized entanglement wedges can be associated with exact subalgebras of this full algebra.
Comments57 pages + appendices, 7 figures; reference added
