In this paper we review the AdS/BCFT proposal of T. Takayanagi for holographic description of systems with boundaries, in particular, boundary conformal field theories (BCFTs). Motivated by better understanding of the proposed duality we employ entanglement entropy as a probe of familiar properties of impurities and defects. Using the dual gravity description, we check that in two spacetime dimensions the impurity entropy does not depend on a particular state of the theory, which is a well-known CFT result. In three dimensions different, and not necessarily equivalent, definitions of the defect entropy can be given. We compute the entanglement entropy of a line defect at finite temperature and compare it with earlier calculations of the thermodynamical entropy. The results indicate that the entanglement entropy flows to the definition of the entropy as the Bekenstein-Hawking entropy associated to a portion of the black horizon, which we call impurity "shadow". Geometric configurations, which we discuss, provide examples of RG flows of the defect entropies. We outline the connection between the geometric picture of the RG flows and examples of lattice calculations. We also discuss some new generalizations of the AdS/BCFT geometries.

中文翻译：

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AdS/BCFT 中边界熵的研究

在本文中，我们回顾了 T. Takayanagi 的 AdS/BCFT 提案，用于对具有边界的系统进行全息描述，特别是边界共形场理论 (BCFT)。出于对所提出的二元性的更好理解，我们采用纠缠熵作为对杂质和缺陷的熟悉特性的探测。使用双重引力描述，我们检查了在两个时空维度中，杂质熵不依赖于理论的特定状态，这是众所周知的 CFT 结果。在三个不同的维度中，可以给出缺陷熵的定义，但不一定是等价的。我们在有限温度下计算线缺陷的纠缠熵，并将其与热力学熵的早期计算进行比较。结果表明，纠缠熵流向熵的定义，即与黑色地平线的一部分相关联的 Bekenstein-Hawking 熵，我们称之为杂质“阴影”。我们讨论的几何配置提供了缺陷熵的 RG 流的示例。我们概述了 RG 流的几何图形与晶格计算示例之间的联系。我们还讨论了 AdS/BCFT 几何的一些新概括。