标题： 弦理论中的量子纠缠指数 显示英文标题

标题： Quantum Entanglement Index in String Theory

摘要： 我们定义了一个“量子纠缠指数”的概念，旨在使用弦论中的弦式复制方法，在一环阶计算黑洞视界的该指数。 我们考虑BTZ黑洞的视界来构建相关的锥面轨道，由奇数整数$N$标记，并将配分函数作为$N$的函数进行计算，对应于分数索引的Rényi熵。 我们证明即使在场论极限下通常具有紫外发散性，该指数在紫外和红外区域都是无快子且自然有限的。 因此，该指数提供了一种无需在$N$中进行解析延拓即可诊断弦论纠缠结构的有用方法。 显示英文摘要

摘要： We define a notion of `quantum entanglement index' with the aim to compute it for black hole horizons in string theory at one-loop order using the stringy replica method. We consider the horizon of BTZ black holes to construct the relevant conical orbifolds, labeled by an odd integer $N$, and compute the partition function as a function of $N$, corresponding to the fractional indexed R\'enyi entropy. We show that it is free of tachyons and naturally finite both in the ultraviolet and the infrared, even though it is generically ultraviolet divergent in the field theory limit. Thus, the index provides a useful diagnostic of the entanglement structure of string theory without the need for analytic continuation in $N$.