Introduction to Generalized Global Symmetries in QFT and Particle Physics

Abstract

Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the study of particle phenomenology. In these notes we give an exposition to the topic of generalized/categorical symmetries for high energy phenomenologists although the topics covered may be useful to the broader physics community. Here we describe generalized symmetries without the use of category theory and pay particular attention to the introduction of discrete symmetries and their gauging.

74 pages plus appendices

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• Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
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• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
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• Fractionalization of Coset Non-Invertible Symmetry and Exotic Hall Conductance
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
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• Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories
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• Higher-Matter and Landau-Ginzburg Theory of Higher-Group Symmetries
• Monopole Breaking of Chern-Weil Symmetries
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
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• Higher-form symmetry and chiral transport in real-time Abelian lattice gauge theory
• Hydrodynamic fluctuations and topological susceptibility in chiral magnetohydrodynamics
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Higher-form anomalies and state-operator correspondence beyond conformal invariance
• Non-invertible symmetries of two-dimensional Non-Linear Sigma Models
• Generalized symmetry enriched criticality in (3+1)d