Topological Entanglement Entropy of Black Hole Interiors

E. Howard
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引用次数: 2

Abstract

Recent theoretical progress shows that ([Formula: see text]) black hole solution manifests long-range topological quantum entanglement similar to exotic non-Abelian excitations with fractional quantum statistics. In topologically ordered systems, there is a deep connection between physics of the bulk and that at the boundaries. Boundary terms play an important role in explaining the black hole entropy in general. We find several common properties between BTZ black holes and the Quantum Hall effect in ([Formula: see text])-dimensional bulk/boundary theories. We calculate the topological entanglement entropy of a ([Formula: see text]) black hole and recover the Bekenstein–Hawking entropy, showing that black hole entropy and topological entanglement entropy are related. Using Chern–Simons and Liouville theories, we find that long-range entanglement describes the interior geometry of a black hole and identify it with the boundary entropy as the bond required by the connectivity of spacetime, gluing the short-range entanglement described by the area law. The IR bulk–UV boundary correspondence can be realized as a UV low-excitation theory on the bulk matching the IR long-range excitations on the boundary theory. Several aspects of the current findings are discussed.
黑洞内部的拓扑纠缠熵
最近的理论进展表明(公式:见文本)黑洞解表现出类似于具有分数阶量子统计的奇异非阿贝尔激发的长程拓扑量子纠缠。在拓扑有序系统中,体物理和边界物理之间有着深刻的联系。一般来说,边界项在解释黑洞熵方面起着重要的作用。我们在(公式:见原文)维体/边界理论中发现了BTZ黑洞和量子霍尔效应之间的几个共同特性。我们计算了(公式:见文)黑洞的拓扑纠缠熵,并恢复了贝肯斯坦-霍金熵,表明黑洞熵与拓扑纠缠熵是相关的。利用chen - simons和Liouville理论,我们发现远程纠缠描述了黑洞的内部几何形状,并将其与边界熵识别为时空连通性所需的键,粘合了由面积定律描述的短程纠缠。红外体-紫外边界对应可以实现为体上的紫外低激发理论与边界理论上的红外远程激发相匹配。讨论了当前研究结果的几个方面。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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3 weeks
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