标题： 黑洞的纠缠熵 显示英文标题

标题： Entanglement entropy of black holes

摘要： 纠缠熵是一个基本量，它表征了更大量子力学系统中子系统之间的关联。 对于由表面分隔的两个子系统，纠缠熵与该表面的面积成正比，并依赖于调节短距离关联的紫外截止。 当应用于黑洞时，纠缠熵的几何性质尤其引人入胜，此时纠缠表面是黑洞视界。 我回顾了这一计算的各个方面：如具有锥形奇点的空间几何和热核方法等有用的数学工具，熵中的紫外发散及其重整化，以及四维和六维中的对数项及其与共形异常的关系。 综述的重点是锥形奇点方法的系统使用。 详细讨论了与其他已知方法如't Hooft的砖墙模型和光学度规中的欧几里得路径积分之间的关系。 强调了由于非最小耦合到引力的场导致的纠缠熵的令人困惑的行为。 通过二维和四维的例子说明了黑洞视界纠缠熵的全息描述。 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。 显示英文摘要

摘要： 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 the 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 4 and 6 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 black hole 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.