The black hole information puzzle, islands and boundary conformal field theory

该项目的目的是探索霍金的量子黑洞信息丢失之谜的各个方面，以及通过所谓的“岛屿范式”提出的最新解决方案。著名的是，霍金证明黑洞通过发射具有热光谱的辐射蒸发，就像任何热物体一样。然而，纯粹的热谱将与量子力学相冲突，因为量子力学的规则要求辐射携带形成黑洞的量子态的信息。这个难题直到最近（2019年11月）才在近50年后得到解决。所提出的解决方案是基于所谓的岛屿范式，它来自霍金辐射熵（与量子纠缠有关）的微妙量子引力计算。计算表明，老黑洞的Hawking辐射纠缠熵受到连接黑洞内部和外部Hawking辐射的虫洞构型的贡献，在降低熵的过程中再现了所谓的熵的“Page曲线”行为，根据量子力学的规则。这个项目的目标将是了解视界后面的岛屿区域是如何在霍金辐射中编码的。为了理解这一点，我们需要一个真正微观的量子引力描述。虽然这样的描述还不存在，但它可以通过量子引力和没有引力的量子场论（QFT）之间的显着关系获得-称为“全息对偶性”。在这个项目中，我们将使用全息对偶性来映射黑洞蒸发问题到两个时空维度中普通量子场论的相关问题，特别是具有量子力学自由度的边界的共形场论（CFT）。CFT描述了霍金辐射，而边界上的量子系统全息地捕获了黑洞的量子自由度。使用已知的技术检查相关函数在这样的BCFTs（B的边界），我们将提供一个微观描述的岛屿机制的黑洞和信息检索的黑洞。我们的目标将是了解如何通过一些量子操作作用于外部的霍金辐射，影响视界后面岛屿区域的自由度。另一个主要目标是了解真正非平衡环境中的岛机制以及虫洞在此背景下所扮演的角色，这一项目的结果将为霍金辐射中信息关联的微观研究提供一个新的窗口，并加深对引力中固有量子现象的理解。

The aim of this project is to explore aspects of Hawking's information loss puzzle for quantum black holes and its proposed recent resolution via the so-called "island paradigm". Famously, black holes were shown by Hawking to evaporate by emitting radiation with a thermal spectrum just like any hot object. However, a purely thermal spectrum would be in conflict with quantum mechanics as the rules of quantum mechanics require the radiation to carry information of the quantum state that went into making the black hole. This puzzle has only recently (November 2019) met with a potential resolution after nearly five decades. The proposed resolution is based on the so-called island paradigm which emerges from a subtle quantum gravity calculation of the Hawking radiation entropy (associated to quantum entanglement). The calculation shows that the entanglement entropy of Hawking radiation for an old black hole receives contributions from wormhole configurations which link the interior of the black hole to the Hawking radiation outside, in the process lowering the entropy and reproducing the so-called "Page curve" behaviour of the entropy, in accordance with the rules of quantum mechanics.The goal of this project will be to understand how the island regions behind the horizon are encoded in the Hawking radiation. In order to understand this we need a truly microscopic description of quantum gravity. Although such a description does not exist yet, it is available via a remarkable relationship between quantum gravity and quantum field theory (QFT) without gravity -- called "holographic duality". In this project we will use holographic duality to map the black hole evaporation problem to a related problem of ordinary quantum field theory in two spacetime dimensions, specifically a conformal field theory (CFT) with a boundary where quantum mechanical degrees of freedom reside. The CFT describes the Hawking radiation while the quantum system on the boundary holographically captures the quantum degrees of freedom of the black hole. Using known techniques for examining correlation functions in such BCFTs (B for boundary), we will provide a microscopic description of the island mechanism for black holes and information retrieval for black holes. Our goal will be to understand how acting on the Hawking radiation outside with some quantum operations, affects the degrees of freedom in the island regions behind the horizon. Another major goal will be to understand the island mechanism in a genuinely non equilibrium setting and the role played by wormholes in this context.The results of this project will provide a new window into the microscopics of information correlation in Hawking radiation and a deeper understanding of intrinsically quantum phenomena in gravity.