Looking at shadows of entanglement wedges
Looking at shadows of entanglement wedges
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DOI：
10.1093/ptep/ptaa152
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发表时间：
2019-12
影响因子：
3.5
通讯作者：
Yuya Kusuki;Yukiharu Suzuki;T. Takayanagi;Koji Umemoto
中科院分区：
文献类型：
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作者：
Yuya Kusuki;Yukiharu Suzuki;T. Takayanagi;Koji Umemoto
我们提出了一种直接从共形场论（CFT）计算中推导纠缠楔形状的新方法。我们指出全息cft中的约化密度矩阵具有一个尖锐的楔形结构，使得楔形内部可以区分两个局部激励，而外部则不能。我们可以通过计算可分辨度来确定这个楔形，我们称之为CFT楔形。我们发现以保真度或布尔斯距离作为可分辨度度量来定义的CFT楔形与反德西特(AdS)/CFT中纠缠楔形的阴影完全吻合。我们证实了二维全息CFT楔和纠缠楔之间的一致性，其中子系统被选择为间隔或双间隔，以及具有圆球子系统的高维CFT。另一方面，如果我们考虑一个自由标量CFT，我们发现没有尖锐的CFT楔。这表明，由于大N分解，尖锐的纠缠楔只在全息cft中出现。我们还将我们的分析推广到一个时间相关的例子和全息边界共形场理论（AdS/BCFT）。最后，我们研究了其他可区分性度量来定义CFT楔形。我们观察到，一些措施导致CFT楔子与AdS/CFT中的纠缠楔子略有偏离，我们对此给出了启发式解释。这篇论文是我们早期信件（arXiv:1908.09939 [help -th]）的扩展版本，包括各种新的观察和例子。
We present a new method of deriving shapes of entanglement wedges directly from conformal field theory (CFT) calculations. We point out that a reduced density matrix in holographic CFTs possesses a sharp wedge structure such that inside the wedge we can distinguish two local excitations, while outside we cannot. We can determine this wedge, which we call a CFT wedge, by computing a distinguishability measure. We find that CFT wedges defined by the fidelity or Bures distance as a distinguishability measure coincide perfectly with shadows of entanglement wedges in anti-de Sitter (AdS)/CFT. We confirm this agreement between CFT wedges and entanglement wedges for two-dimensional holographic CFTs where the subsystem is chosen to be an interval or double intervals, as well as higher-dimensional CFTs with a round ball subsystem. On the other hand, if we consider a free scalar CFT, we find that there are no sharp CFT wedges. This shows that sharp entanglement wedges emerge only for holographic CFTs owing to the large-$N$ factorization. We also generalize our analysis to a time-dependent example and to a holographic boundary conformal field theory (AdS/BCFT). Finally, we study other distinguishability measures to define CFT wedges. We observe that some of the measures lead to CFT wedges which slightly deviate from the entanglement wedges in AdS/CFT, and we give a heuristic explanation for this. This paper is an extended version of our earlier letter (arXiv:1908.09939 [hep-th]) and includes various new observations and examples.