论文标题
时空纠缠熵：协方差和离散性
Spacetime Entanglement Entropy: Covariance and Discreteness
论文作者
论文摘要
我们回顾了Sorkin在连续体和类似歧管的因果集中的自由量子标量场的Sorkin的时空表述（SSEE）。 2D缸时空中的因果钻石的SSEE已被证明具有卡拉列赛的形式，而对于de Sitter和Schwarzschild de Sitter Horizons in Dimensions $ d> 2 $，它与模式的Von-neumann Entropy匹配。在这些连续示例中，SSEE通过施加紫外线切割来调节。类似歧管的因果集有天然的协变时空截止，因此为研究调节的QFT提供了一个竞技场。但是，已显示出$ d = 2 $和$ d = 4 $的不同流形的SSEE（例如因果集）展示了卷而不是区域法律。仅当在模仿连续性行为的频谱的缩放率中实现额外的紫外线切口时才能恢复该区域定律。我们讨论了这些结果的含义，并表明体积法可能是因果集的基本非本地性和新紫外线物理学的迹象的表现。
We review some recent results on Sorkin's spacetime formulation of the entanglement entropy (SSEE) for a free quantum scalar field both in the continuum and in manifold-like causal sets. The SSEE for a causal diamond in a 2d cylinder spacetime has been shown to have a Calabrese-Cardy form, while for de Sitter and Schwarzschild de Sitter horizons in dimensions $d>2$, it matches the mode-wise von-Neumann entropy. In these continuum examples the SSEE is regulated by imposing a UV cut-off. Manifold-like causal sets come with a natural covariant spacetime cut-off and thus provide an arena to study regulated QFT. However, the SSEE for different manifold like causal sets in $d=2$ and $d=4$ has been shown to exhibit a volume rather than an area law. The area law is recovered only when an additional UV cut-off is implemented in the scaling regime of the spectrum which mimics the continuum behaviour. We discuss the implications of these results and suggest that a volume-law may be a manifestation of the fundamental non-locality of causal sets and a sign of new UV physics.
