Chaos and coarse-graining in holography: towards a new paradigm for quantum gravity

量子引力中黑洞的新范式正在出现。它受到规范/重力二象性（“全息”）的一般框架的启发，它允许在双非引力量子多体系统方面对量子引力进行一致的定义。更具体地说，新范式将植根于近年来的加速发展，因为：(i)将量子信息理论的概念和方法纳入我们使用全息二象性的方式，以及（ii）发现新的二象性模型，这些模型的研究前所未有地简单，但仍然表现出对量子引力感兴趣的关键特征。有了这些强大的新工具，一个一致的量子黑洞理论就指日可待了。我的建议的中心目标是：（*）在量子黑洞及其双多体系统中建立一个全面和统一的热化、耗散、混沌和随机性理论。（*）确定对偶映射和量子引力下基本量子场论约束（统一性、解析性、热性约束等）的命运。（*）根据双系统的自由度找到黑洞内部的详细模型。工作包包括研究保形和无序系统中的量子混沌，量子引力中系综平均的作用，以及流体力学背景下波动黑洞的有效描述。我的方法是量身定制的，以协同我所建立的重力，量子场论和非平衡动力学方面的专业知识的独特组合：我将使用基于对称性的方法和有效的场论方法，以统一，一般和计算效率的方式使二元性的关键方面显现出来。我的方法旨在确定量子引力的普遍方面，从而导致超越二元性甚至宇宙学背景的新见解。

A new paradigm is emerging for black holes in quantum gravity. It is inspired by the general framework of gauge/gravity duality ('holography'), which allows for a consistent definition of quantum gravity in terms of dual non-gravitational quantum many-body systems. More concretely, the new paradigm will be rooted in an acceleration of developments in recent years due to: (i) the incorporation of quantum information theoretic concepts and methods into the way we use the holographic duality, and (ii) the discovery of new models of the duality which are unprecedentedly simple to study but nevertheless exhibit the key features of interest in quantum gravity. Armed with these powerful new tools, a consistent theory of quantum black holes is now within reach. Central objectives of my proposal are: (*) Develop a comprehensive and unifying theory of thermalization, dissipation, chaos, and randomness in quantum black holes and their dual many-body systems. (*) Determine the fate of fundamental quantum field theory constraints (unitarity, analyticity, thermality constraints,...) under the duality map and in quantum gravity. (*) Find a detailed model of black hole interiors in terms of degrees of freedom in the dual system. Work packages include investigations of quantum chaos in conformal and in disordered systems, the role of ensemble averages in quantum gravity, and an effective description of fluctuating black holes in the context of hydrodynamics. My methodology is tailored to synergize the unique combination of expertise in gravity, quantum field theory, and non-equilibrium dynamics that I have established: I will use a symmetry-based approach and effective field theory methods to make crucial aspects of the duality manifest in a unifying, general, and computationally efficient fashion. My approach is designed to identify universal aspects of quantum gravity and will thus lead to new insights that are generalizable beyond the context of the duality and even in cosmology.