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Comments on defining entanglement entropy
Nuclear Physics B ( IF 2.8 ) Pub Date : 2020-07-30 , DOI: 10.1016/j.nuclphysb.2020.115118
Jennifer Lin , Đorđe Radičević

We revisit the issue of defining the entropy of a spatial region in a broad class of quantum theories. In theories with explicit regularizations, working within an elementary but general algebraic framework applicable to matter and gauge theories alike, we give precise path integral expressions for three known types of entanglement entropy that we call full, distillable, and gauge-invariant. For a class of gauge theories that do not necessarily have a regularization in our framework, including Chern-Simons theory, we describe a related approach to defining entropies based on locally extending the Hilbert space at the entangling edge, and we discuss its connections to other calculational prescriptions. Based on results from both approaches, we conjecture that it is always the full entanglement entropy that is calculated by standard holographic techniques in strongly coupled conformal theories.



中文翻译:

关于定义纠缠熵的评论

我们将重新讨论在广泛的量子理论中定义空间区域的熵的问题。在具有显式正则化的理论中,在适用于物质和规范理论的基本但通用的代数框架内工作,我们为三种已知的纠缠熵给出了精确的路径积分表达式,我们称其为完全,可蒸馏和规范不变。对于一类在我们的框架中不一定具有正则化的量规理论,包括Chern-Simons理论,我们描述了一种基于在纠缠边缘局部扩展Hilbert空间来定义熵的相关方法,并讨论了它与其他方法的联系。计算处方。根据两种方法的结果,

更新日期:2020-08-06
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