arXiv 2401.016532024-01-03hep-th

$d$维弯曲背景中的岛与纠缠熵

Islands and entanglement entropy in $d$-dimensional curved backgrounds

Filip Landgren, Arvind Shekar

AI总结：

本文研究了$d$维AdS黑洞背景下的纠缠岛，证明模拟Hawking辐射的量子场需从共形母理论继承尺度，并发现当$d>2$时岛永远不会出现。

摘要：

关于纠缠岛的讨论大部分集中在$2d$ JT引力与耦合到$2d$ CFT的平直热浴的特定设置上。在本文中，我们考虑了在$d$维AdS黑洞背景中对岛的更一般设置和处理。模拟Hawking辐射的量子场具有尺度，并从共形母理论中一致地继承而来；因此它们的对称性与弯曲背景的对称性兼容。我们明确证明了岛的存在对用于模拟Hawking辐射的CFT的选择敏感。我们计算了零温下$d$维负曲率背景上共形场的重整化纠缠熵，以及UV边界附近纠缠区的热正则化熵。使用后一个量作为Hawking辐射的熵，我们发现对于$d>2$，岛永远不会出现。

英文摘要：

A large part of the discussion on entanglement islands has explored the specific setup of $2d$ JT gravity with a flat heatbath coupled to a $2d$ CFT. In this paper, we consider a more general setup and treatment of islands in a $d-$dimensional AdS black hole background. The quantum fields modeling the Hawking radiation have a scale and are consistently inherited from a conformal parent theory; their symmetries are thus compatible with those of curved backgrounds. We demonstrate explicitly that the existence of islands is sensitive to the choice of CFT used to model the Hawking radiation. We compute the renormalised entanglement entropy of conformal fields on a negatively curved background in $d$ dimensions at zero temperature as well as the thermal regulated entropy of an entangling region near the UV boundary. Using the latter quantity as the entropy of the Hawking radiation, we find that islands never emerge for $d>2$.

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