AdS${}_3$ 面积网络中的链路面积对易子
Link-area commutators in AdS${}_3$ area-networks
AI总结：
本文通过构建极值表面网络并计算链路面积对易子，探究纯AdS3引力中抑制HRT面积量子涨落的阻碍，发现特定4链路网络面积可对易，但更一般网络通常呈非阿贝尔代数。
摘要：
随机张量网络（RTNs）已被证明是建立 AdS/CFT 对应模型的有效工具。由于其平坦的纠缠谱，在讨论给定的边界区域 $R$ 及其补集 $\bar R$ 时，标准 RTNs 最类似于体量子引力理论的固定面积态，在该态中相应 HRT 表面的面积量子涨落已被抑制。然而，此类 RTNs 对所有 $R, \bar R$ 的选择均具有平坦的纠缠谱，而多个 HRT 面积的量子涨落只有在相应的 HRT 面积算符相互对易时才能被抑制。我们通过构建链路为余维 2 极值表面的网络，并显式计算相关链路面积的半经典对易子，来探究纯 AdS$_3$ Einstein-Hilbert 引力中此类阻碍的严重程度。由于 $d=3$，余维 2 极值表面即为测地线，且余维 2 的“面积”即为长度。我们发现了一个由 HRT 表面和 Chen-Dong-Lewkowycz-Qi 约束 HRT 表面定义的简单 4 链路网络，其所有链路面积均对易。然而，更一般网络的链路面积生成的代数往往是非阿贝尔的。其中一个此类非阿贝尔示例与纠缠楔截面相关，可能具有更普遍的意义。
英文摘要：
Random tensor networks (RTNs) have proved to be fruitful tools for modelling the AdS/CFT correspondence. Due to their flat entanglement spectra, when discussing a given boundary region $R$ and its complement $\bar R$, standard RTNs are most analogous to fixed-area states of the bulk quantum gravity theory, in which quantum fluctuations have been suppressed for the area of the corresponding HRT surface. However, such RTNs have flat entanglement spectra for all choices of $R, \bar R,$ while quantum fluctuations of multiple HRT-areas can be suppressed only when the corresponding HRT-area operators mutually commute. We probe the severity of such obstructions in pure AdS$_3$ Einstein-Hilbert gravity by constructing networks whose links are codimension-2 extremal-surfaces and by explicitly computing semiclassical commutators of the associated link-areas. Since $d=3,$ codimension-2 extremal-surfaces are geodesics, and codimension-2 `areas' are lengths. We find a simple 4-link network defined by an HRT surface and a Chen-Dong-Lewkowycz-Qi constrained HRT surface for which all link-areas commute. However, the algebra generated by the link-areas of more general networks tends to be non-Abelian. One such non-Abelian example is associated with entanglement-wedge cross sections and may be of more general interest.
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