论文标题
与副本的乐趣：张量网络和重力中的三方
Fun with replicas: tripartitions in tensor networks and gravity
论文作者
论文摘要
我们为三方纯净的状态引入了一种新的相关措施，我们称为$ g（a：b：c）$。相对于子系统$ a $，$ b $，$ c $，在本地一职下不变的数量是对称的，并且以$ \ log d_a d_a d_b $为界。对于随机张量的网络状态，我们证明$ g（a：b：c）$等于张量网络的最小三级运动的大小，即，最小切口的对数债券维度将网络分为三个组件，用$ a $ a $，$ b $和$ c $和$ c $。我们认为，对于具有固定空间几何形状的全息状态，$ g（a：b：c）$同样由最小面积的三人区计算。对于一般的全息状态，$ g（a：b：c）$是由反反应几何形状中最小的三阶层确定的，但是平滑的版本等于在未来的领先顺序中以无偿反应的几何形状中的最小三站。我们简要讨论一个天然数量$ g_n（a：b：c）$ for integer $ n \ geq 2 $ clementize $ g = g_2 $。在全息图中，$ g_n的计算（a：b：c）$ for $ n> 2 $自发破坏了$ \ mathbb {z} _n \ times \ times \ times \ mathbb {z} _n $ replica symmetry的一部分。这样可以防止在假设的分析延续至$ n = 1 $的情况下，Lewkowycz-Maldacena Trick的任何天真应用。
We introduce a new correlation measure for tripartite pure states that we call $G(A:B:C)$. The quantity is symmetric with respect to the subsystems $A$, $B$, $C$, invariant under local unitaries, and is bounded from above by $\log d_A d_B$. For random tensor network states, we prove that $G(A:B:C)$ is equal to the size of the minimal tripartition of the tensor network, i.e., the logarithmic bond dimension of the smallest cut that partitions the network into three components with $A$, $B$, and $C$. We argue that for holographic states with a fixed spatial geometry, $G(A:B:C)$ is similarly computed by the minimal area tripartition. For general holographic states, $G(A:B:C)$ is determined by the minimal area tripartition in a backreacted geometry, but a smoothed version is equal to the minimal tripartition in an unbackreacted geometry at leading order. We briefly discuss a natural family of quantities $G_n(A:B:C)$ for integer $n \geq 2$ that generalize $G=G_2$. In holography, the computation of $G_n(A:B:C)$ for $n>2$ spontaneously breaks part of a $\mathbb{Z}_n \times \mathbb{Z}_n$ replica symmetry. This prevents any naive application of the Lewkowycz-Maldacena trick in a hypothetical analytic continuation to $n=1$.
