黑洞的纠缠熵

IF 26.3 2区 物理与天体物理 Q1 PHYSICS, PARTICLES & FIELDS
Sergey N. Solodukhin
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引用次数: 461

摘要

纠缠熵是一个基本的量,它表征了一个更大的量子力学系统中子系统之间的相关性。对于被表面分隔的两个子系统,纠缠熵与表面面积成正比,并依赖于紫外截止,紫外截止调节了短距离相关。当纠缠面为黑洞视界时,纠缠熵计算的几何性质特别有趣。我回顾了这一计算的各个方面:有用的数学工具,如圆锥奇点空间的几何和热核方法,熵的UV散度及其重整化,四维和六维纠缠熵的对数项及其与共形异常的关系。本文的重点是对圆锥奇异性方法的系统应用。详细讨论了它与其他已知方法的关系,如Hooft的砖墙模型和光学度量中的欧几里得路径积分。强调了纠缠熵在非最小耦合场作用下的令人困惑的行为。用二维和四维的例子说明了黑洞视界的纠缠熵的全息描述。最后,我考察了将贝肯斯坦-霍金熵完全解释为纠缠熵的可能性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Entanglement Entropy of Black Holes

The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as ’t Hooft’s brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the blackhole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.

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来源期刊
Living Reviews in Relativity
Living Reviews in Relativity 物理-物理:粒子与场物理
CiteScore
69.90
自引率
0.70%
发文量
0
审稿时长
20 weeks
期刊介绍: Living Reviews in Relativity is a peer-reviewed, platinum open-access journal that publishes reviews of research across all areas of relativity. Directed towards the scientific community at or above the graduate-student level, articles are solicited from leading authorities and provide critical assessments of current research. They offer annotated insights into key literature and describe available resources, maintaining an up-to-date suite of high-quality reviews, thus embodying the "living" aspect of the journal's title. Serving as a valuable tool for the scientific community, Living Reviews in Relativity is often the first stop for researchers seeking information on current work in relativity. Written by experts, the reviews cite, explain, and assess the most relevant resources in a given field, evaluating existing work and suggesting areas for further research. Attracting readers from the entire relativity community, the journal is useful for graduate students conducting literature surveys, researchers seeking the latest results in unfamiliar fields, and lecturers in need of information and visual materials for presentations at all levels.
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