Generalized Symmetries in Quantum Field Theory and Quantum Gravity

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.