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

量子引力中的黑洞正在出现一种新的范式。它的灵感来自规范/引力二元性(全息)的一般框架，该框架允许在双重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，新的范式将植根于近年来的加速发展，原因是：(I)将量子信息理论的概念和方法纳入我们使用全息对偶的方式中，以及(Ii)发现了新的对偶模型，这些模型研究起来前所未有地简单，但仍然展示了对量子引力感兴趣的关键特征。有了这些强大的新工具，量子黑洞的一致理论现在已经触手可及。我的提议的中心目标是：(*)发展一个关于量子黑洞及其双重多体系统中的热化、耗散、混沌和随机性的全面和统一的理论。(*)决定基本量子场论约束的命运(一元性、解析性、热性约束，...)在二元图和量子引力下。(*)根据对偶系统中的自由度找到黑洞内部的详细模型。工作包包括研究共形和无序系统中的量子混沌，系综平均在量子引力中的作用，以及在流体力学背景下对波动黑洞的有效描述。我的方法论是为协同我在重力、量子场论和非平衡动力学方面的独特专业知识而量身定做的：我将使用基于对称的方法和有效的场论方法，以统一、通用和计算高效的方式展示二元性的关键方面。我的方法旨在确定量子引力的普遍方面，因此将导致新的见解，这些见解可以超越二元性的背景，甚至在宇宙学中得到推广。

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.