Applications of Generalized Symmetries and Topological Defects to Quantum Matter: September 9 – 13, 2024

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Organizing by:

• Lakshya Bhardwaj (University of Oxford)
• Xie Chen (Caltech)
• Wenjie Ji (Caltech)
• Apoorv Tiwari (Neils Bohr Institute)
• Xiao-Gang Wen (MIT)

Symmetry is arguably the central pillar of theoretical physics. Its applications are ubiquitous, ranging from constraining the particle content of the Standard Model to underpinning Landau’s classification of phases of quantum matter. In the last decade, we have seen a paradigm shift in the understanding of global symmetries in systems of many quantum particles and quantum field theory, with the discovery of many novel generalized symmetry structures: higher-form, higher-group, categorical, non-invertible and subsystem symmetries to name a few. The fundamental observation behind this proliferation of generalized symmetries is that defects exhibiting topological properties in spacetime share many of the essential properties with traditional symmetries, and thus become generalizations of symmetries.

More recently, in the last few years, tremendous progress has been made in understanding the general mathematical structure underlying the description of these symmetries, leading to the outcome that they can be given a unified description in terms of higher-categorical structures in mathematics. However, we have only begun to scratch the surface of possible physical applications of generalized symmetries. The aim of the proposed workshop is to explore applications of gener-alized symmetries and the associated mathematical framework developed to describe topological defects to quantum matter systems.

For this purpose, we believe it would be critical to have a fruitful cross-fertilization of ideas between the theoretical physics communities working on generalized symmetries (in quantum field theory and lattice models) and the wider quantum matter community including those working on numerical studies and experiments, and this workshop aims to provide a stage for such a cross-disciplinary activity.