Generalized Symmetries in Quantum Field Theory and Quantum Gravity

对称性是物理学中最基本的概念之一，解决了一些核心问题，如量子系统的相结构，以及量子引力的一致性。在过去的几年里，我们看到了一个意想不到的爆炸，它可以构成量子理论的对称性。对称的广义概念包括高形式对称，与普通对称相比，其带电对象是高维的（例如Wilson或t Hooft线算子），高群（捕获高形式对称之间的相互作用），更一般地说，分类对称，子系统对称（局部化，例如分数阶）和不可逆转的对称。这些广义对称结构具有真正的物理意义：它们为规范理论中的约束提供了有序参数，通过t Hooft异常约束重整化群流，并表征了低维拓扑秩序。然而，一个完整的理论框架还没有出现，物理意义的全部广度还有待探索。鉴于对称性的核心重要性，本项目的主要目标是提供这些广义对称结构的全面表征，并研究它们对场论真空结构的物理含义。该项目有两个主要部分：一半的研究小组将使用高能和凝聚态物理的见解来研究场论方法。下半部分将探讨弦理论、全息术中强耦合场论背景下的广义对称结构，以及它们在量子引力中的含义，如弱引力猜想和完备性猜想的扩展。该项目将充分利用高能物理、凝聚态物质、数学和量子引力之间的协同作用，探索量子理论中这些新对称性的物理学。

Symmetries are one of the most fundamental concepts in physics, addressing some of the core questions, such as the phase structure of quantum systems, as well as the consistency of quantum gravity. The past few years have seen an unexpected explosion of what can comprise a symmetry of a quantum theory. Generalized notions of symmetry include higher-form symmetries, whose charged objects, in contrast to ordinary symmetries, are higher-dimensional (e.g. Wilson or 't Hooft line operators), higher-groups (which capture the interplay between higher-form symmetries) and, more generally, categorical symmetries, sub-system symmetries (which are localized, e.g. in fracton order) and non-invertible symmetries. These generalized symmetry structures have genuine physical implications: they provide order parameters for confinement in gauge theories, constrain renormalization group flows by 't Hooft anomalies, and characterize low di- mensional topological order. However, a complete theoretical framework has yet to emerge, and the full breadth of physical implications are yet to be explored. Given the central importance of symmetries, the main goal of this project is to provide a comprehensive characterization of these generalized symmetry structures, and to study their physical implications upon the vacuum structure of field theories. The project has two main tranches: half of the research group will work on field theoretic approaches, using insights from high energy and condensed matter physics. The second half will explore generalized symmetry structures in the context of strongly-coupled field theories from string theory, holography, as well as their implications in quantum gravity, such as extensions of the weak gravity gravity conjecture and completeness conjectures. The project will draw strongly from the synergy between higher energy physics, condensed matter, mathematics, and quantum gravity, to explore the physics of these new symmetries in quantum theory.