From path integrals to tensor networks for the AdS/CFT correspondence
From path integrals to tensor networks for the AdS/CFT correspondence
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DOI：
10.1103/physrevd.95.066004
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发表时间：
2016-09
影响因子：
5
通讯作者：
Masamichi Miyaji;T. Takayanagi;Kento Watanabe
中科院分区：
文献类型：
--
作者：
Masamichi Miyaji;T. Takayanagi;Kento Watanabe
本文从两个不同的角度讨论了$\ mathm {AdS}/\ mathm {CFT}$的张量网络描述。首先，我们从具有UV截止的基态波函数的欧几里得路径积分计算开始。我们考虑通过使其紫外截止位置依赖并定义每个长度尺度上的量子态来实现其高效优化。我们推测这个路径积分对应于一个反德西特时空的时间片。接下来，我们根据对偶二维共形场论（CFT），通过重写${\ mathm {AdS}}_{3}$的杀死向量的作用，推导出量子态流。这两种方法都支持${\ mathm {AdS}}_{3}$中的双曲时间片${\ mathm {H}}_{2}$与连续多尺度纠缠重整化分析之间的对应关系。我们还给出了一个启发式论证，说明为什么我们可以期望全息cft具有亚ads尺度的大块局部性。
In this paper, we discuss tensor network descriptions of $\mathrm{AdS}/\mathrm{CFT}$ from two different viewpoints. First, we start with a Euclidean path-integral computation of ground state wave functions with a UV cutoff. We consider its efficient optimization by making its UV cutoff position dependent and define a quantum state at each length scale. We conjecture that this path integral corresponds to a time slice of anti--de Sitter (AdS) spacetime. Next, we derive a flow of quantum states by rewriting the action of Killing vectors of ${\mathrm{AdS}}_{3}$ in terms of the dual two-dimensional conformal field theory (CFT). Both approaches support a correspondence between the hyperbolic time slice ${\mathrm{H}}_{2}$ in ${\mathrm{AdS}}_{3}$ and a version of continuous multiscale entanglement renormalization ansatz. We also give a heuristic argument about why we can expect a sub-AdS scale bulk locality for holographic CFTs.