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

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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.