标题： 全息纠缠熵在Spi处 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：一个红外尺度控制子区域的大小，一个紫外截断。 在AdS/CFT中，红外尺度是AdS长度尺度，紫外截断是体空间径向截断，而子区域由无量纲角度指定。 这是决定AdS/CFT中Ryu-Takayanagi曲面及其面积的数据。 我们认为在渐近平坦空间中存在一个可以与空间无限远（spi）关联的“spi-子区域”概念。 尽管几何上与AdS子区域非常不同，但这种角度数据具有关键特征，即它可以被解释为对spi的二分法。 因此，与spi-子区域相关的RT曲面的面积可以被解释为在该二分法下体态约化密度矩阵的纠缠熵，正如在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部。 在空的平直空间中，它们退化为Rindler视界，并且是Casini、Huerta & Myers所研究的AdS-Rindler视界的类似物。 我们将这些定义与之前关于空空间中锚定在屏幕上的最小曲面的研究联系起来，但也将讨论推广到体空间中有黑洞的情况。 黑洞RT曲面随着spi-子区域的变化而出现的不同相位自然地与AdS中黑洞（小和大）的相位相连接。 一个关键观察是，在平直空间中径向截断与红外尺度相关——事实上没有紫外发散。 我们认为这与之前的建议一致，即在亚AdS尺度下全息对偶是红外/红外对应，并且自由度是{\em 不是}那些局部QFT的自由度，但那些长弦的自由度。 弦当然是著名的紫外有限的。 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 definitions 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.