标题： 螺旋度熵的全息纠缠熵 显示英文标题

标题： A Holographic Entanglement Entropy at Spi

摘要： 定义量子场论中子区域的有限纠缠熵需要引入两个逻辑上独立的尺度：控制子区域大小的红外（IR）尺度和紫外截断（UV cutoff）。在AdS/CFT中，IR尺度是AdS长度尺度，UV截断是体积径向截断，而子区域由无量纲角度指定。这是确定Ryu-Takayanagi曲面及其面积的数据。我们论证，在渐近平坦空间中存在一个可以与空间无穷大（spi）关联的“spi子区域”概念。尽管几何上与AdS子区域有很大不同，但这种角度数据具有关键特性，即允许将其解释为空间无穷大的双划分。因此，与spi子区域相关的RT曲面的面积可以解释为体积态在该双划分下的约化密度矩阵的纠缠熵，就像在AdS/CFT中一样。对于对称的spi子区域，这些RT曲面是渐近因果钻石的腰。在空的平坦空间中，它们退化为Rindler视界，并且是Casini、Huerta和Myers提出的AdS-Rindler视界的类比。我们将这些结果与之前关于空空间中锚定屏幕的极小曲面的工作联系起来，但也推广了讨论到体积中存在黑洞的情况。当改变spi子区域时，黑洞RT曲面的相位自然与AdS中的黑洞（小的和大的）的相位相连。一个关键观察是径向截断与平坦空间中的IR尺度相关联——实际上不存在UV发散。我们论证这与先前的建议一致，即在亚AdS尺度下，全息对偶是一种IR/IR对应关系，并且自由度是{\em 不是}，即局部QFT的自由度，但也是长弦的自由度。当然，众所周知，弦在UV下是有限的。 显示英文摘要

摘要： Defining finite entanglement entropy for a subregion in quantum field theory requires the introduction of two logically independent scales: an IR scale that controls the size of the subregion, and a UV cut-off. In AdS/CFT, the IR scale is the AdS lengthscale, the UV cut-off is the bulk radial cut-off, and the subregion is specified by dimensionless angles. This is the data that determines Ryu-Takayanagi surfaces and their areas in AdS/CFT. We argue that in asymptotically flat space there exists the notion of a ``spi-subregion" that one can associate to spatial infinity (spi). Even though geometrically quite different from an AdS subregion, this angle data has the crucial feature that it allows an interpretation as a bi-partitioning of spi. Therefore, the area of the RT surface associated to the spi-subregion can be interpreted as the entanglement entropy of the reduced density matrix of the bulk state under this bi-partition, as in AdS/CFT. For symmetric spi-subregions, these RT surfaces are the waists of Asymptotic Causal Diamonds. In empty flat space they reduce to Rindler horizons, and are analogues of the AdS-Rindler horizons of Casini, Huerta \& Myers. We connect these results to previous work on minimal surfaces anchored to screens in empty space, but also generalize the discussion to the case where there are black holes in the bulk. The phases of black hole RT surfaces as the spi-subregion is varied, naturally connect with those of black holes (small and large) in AdS. A key observation is that the radial cut-off is associated to an IR scale in flat space -- and in fact there are no UV divergences. We argue that this is consistent with previous suggestions that in sub-AdS scales the holographic duality is an IR/IR correspondence and that the degrees of freedom are {\em not} those of a local QFT, but those of long strings. Strings are of course, famously UV finite.