Local Holography and Quantum Gravity

我们对物理宇宙的理解建立在两个基石上：量子力学和广义相对论。量子力学用统计概念来描述亚原子粒子的行为。相比之下，广义相对论，即爱因斯坦的引力理论，利用时空几何在天文尺度上提供了一种优雅的物理描述。将这两种不同的自然观统一在一个称为“量子引力”的框架中，仍然是21世纪理论物理学家面临的突出的基本问题。我们对这个问题的看法正处于彻底转变的边缘。在过去的六年里，越来越清楚的是，一个新的组织原理正在变得可行：引力物理的对称性概念。自物理学开始以来，对称性一直是理解基础物理学的主要组织工具，也是过去许多突破的主要因素。对称通常使我们能够理解宇宙的基本组成部分。对称也是我们唯一可靠的理论指南，它让我们从经典走向量子而不会迷失方向。在过去的5年里，我的工作揭示了用一种新的对称群来理解引力动力学的关键方面是可能的。这开启了获取量子引力核心难题新信息的可能性，例如：基本的引力自由度是什么？它们与量子物质相互作用的本质是什么？我的研究计划建立在这些结果的基础上，开发一种新的量子引力范式，称为局部全息。这个程序的目的是充分展示组织引力动力学的全对称群。它旨在证明经典几何和引力动力学可以根据这种新的对称原理进行重塑。这样做最终将使我们能够以一种与量子力学兼容的方式理解时空几何。最后，这一探索将使我们能够开发新的数学和概念工具，最终将量子引力的不同方法，如AdS/CFT，天体全息学和非微扰量子引力，在对称的保护和指导下结合起来。这项研究将吸引优秀的学生，并在一个令人兴奋的多学科环境中培养他们。他们将发展编程、沟通、领导和解决问题的技能，这些技能对学术界和许多工业部门都是必要的。

Our understanding of the physical universe rests on two cornerstones: Quantum mechanics and general relativity. Quantum mechanics describes subatomic particles using statistical notions to describe their behavior. In contrast general relativity, Einstein's theory of gravity, provides an elegant description of physics on astronomical scales using spacetime geometry. Unifying these two dissimilar views of nature in a single framework called "quantum gravity'' remains the outstanding fundamental question for theoretical physicist in the twenty-first century. We are now on the verge of a radical transformation in our thinking about this problem. Over the past six years, it has become increasingly clear that a new organizational principle is becoming available: the concept of symmetries for gravitational physics. Since the beginning of physics, symmetries have been the primary organizational tool for understanding fundamental physics and the leading factor in many past breakthroughs. Symmetry usually allows us to understand the fundamental building blocks of our universe. Symmetry is also our only reliable theoretical guide allowing us to go from the classical to the quantum without getting lost. In the past 5 years, my work has revealed that it is possible to understand key aspects of gravitational dynamics in terms of a new kind of symmetry groups. This opens the possibility of accessing new information about the central conundrums of quantum gravity, such as : What are the fundamental gravitational degrees of freedom? What is the nature of their interaction with quantum matter? My research proposal builds on these results to develop a new paradigm for quantum gravity called Local Holography. This program aims to reveal in its full glory the full symmetry group organizing gravitational dynamics. It aims to prove that classical geometry and gravitational dynamics can be recast in terms of this new symmetry principle. Doing so will finally allow us to understand spacetime geometry in a way compatible with quantum mechanics. Finally, this quest will allow us to develop new mathematical and conceptual tools that finally bring together the different approaches to quantum gravity, such as AdS/CFT, Celestial Holography, and non-perturbative quantum gravity, under the umbrella and guidance of symmetry. This research will attract excellent students and train them in an exciting multidisciplinary environment. They will develop programming, communication, leadership, and problem-solving skills, which are necessary for academia and transferable to many industry sectors.