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

黑洞的量子方面对理论物理学提出了挑战，其形式是爱因斯坦广义相对论的崩溃或与量子力学和量子信息理论的基本原理的明显紧张关系。重要的谜题包括对解释黑洞熵的微观状态的详细理解，事件视界后面的坠落观察者的经验，以及时空奇点的解决方案。作为回答这些问题的一步，我的项目旨在确定量子引力基本理论的普遍方面和粗粒度印记。规范/引力对偶性的背景为这些想法提供了一个详细的测试基础。这种对偶性表明，在某些情况下，量子引力和黑洞在非引力量子场论中具有等价的对偶描述，其规则和基本定律原则上是很好理解的。（量子）引力和量子多体系统之间令人惊讶和深刻的联系使这项研究非常令人兴奋，并导致许多可能的应用。特别是，通过对对偶性的字典进行解码，并找到一种使对偶性的某些方面更加明显的数学描述，我将阐明基本的和普遍的量子场论约束对引力理论的影响。相反，我还将开发一种数学语言，适合以系统的方式对这些约束进行编码，目标是有效地识别和计算双量子多体系统中黑洞物理学的标志性特征。

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.