Physicists are rewriting the rules of what a symmetry can be in quantum theory. For decades, symmetries meant simple transformations—like rotating a crystal or flipping a particle’s charge. But recent work has revealed far stranger types: symmetries that act on lines or surfaces rather than points, symmetries that cannot be reversed, and symmetries that only apply to subsystems of a material. These "generalized symmetries" already explain how quarks become confined inside protons and how certain exotic materials conduct electricity only on their edges. Yet no complete theory exists to describe them all. This project aims to build that framework, using tools from high-energy physics, condensed matter, string theory, and mathematics. Half the team will develop field-theoretic models; the other half will test these ideas in strongly coupled theories from string theory and holography, and explore what they imply for quantum gravity—for instance, whether they extend the weak gravity conjecture. The work is fundamental science with no immediate practical application. But past revolutions in symmetry have underpinned the Standard Model of particle physics and the discovery of topological phases of matter, which now inform quantum computing research. A deeper understanding of generalized symmetries could similarly reshape how we think about the fabric of reality.
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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.
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