Chaos, Randomness, Coarse-Graining: Towards a New Paradigm for Holography

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Quantum aspects of black holes present challenges to theoretical physics in the form of a breakdown of Einstein's theory of general relativity or apparent tensions with basic principles of quantum mechanics and quantum information theory. Important puzzles include a detailed understanding of the microscopic states accounting for the entropy of a black hole, the experience of an infalling observer behind the event horizon, and a resolution of the spacetime singularity. As a step towards answering such questions, my project aims to identify universal aspects and coarse-grained imprints of a fundamental theory of quantum gravity. The context of gauge/gravity duality provides a detailed testing ground for such ideas. The duality states that in certain situations quantum gravity and black holes have an equivalent dual description in terms of a non-gravitational quantum field theory whose rules and basic laws are in principle well understood. This surprising and deep connection between (quantum) gravity and quantum many-body systems makes this research very exciting and leads to many possible applications. In particular, by decoding the dictionary of the duality and by finding a mathematical description that makes some aspects of it more manifest, I will elucidate the imprint of fundamental and universal quantum field theory constraints on the gravitational theory. Conversely, I will also develop a mathematical language that is suitable to encode such constraints in a systematic way with the goal to efficiently identify and calculate hallmark signatures of black hole physics in the dual quantum many-body systems.