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Simons Lectures on Categorical Symmetries
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Global Categorical Symmetries are a powerful new tool for analyzing quantum field theories. This volume compiles lecture notes from the 2022 and 2023 summer schools on Global Categorical Symmetries, held at the Perimeter Institute for Theoretical Physics and at the Swiss Map Research Station in Les Diableret. Specifically, this volume collects the lectures: * An introduction to symmetries in quantum field theory, Kantaro Ohmori * Introduction to anomalies in quantum field theory, Clay C\'ordova * Symmetry Categories 101, Michele Del Zotto * Applied Cobordism Hypothesis, David Jordan * Finite symmetry in QFT, Daniel S. Freed These volumes are devoted to interested newcomers: we only assume (basic) knowledge of quantum field theory (QFT) and some relevant maths. We try to give appropriate references for non-standard materials that are not covered. Our aim in this first volume is to illustrate some of the main questions and ideas together with some of the methods and the techniques necessary to begin exploring global categorical symmetries of QFTs.
Forward citations
Cited by 9 Pith papers
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Entanglement in Presence of Topological Interfaces and Dualities
Duality interfaces in 2d CFT project the vacuum entanglement spectrum onto a single symmetry sector, making the interface itself a physical symmetry-resolution filter.
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On Quantum Aspects of 1-Form Symmetries II: Bordism, Invertible Phases, and Anomalies
Bordism computation for K(Z,3) identifies a new mixed perturbative anomaly in 5D and a new Z2 discrete anomaly in 7D for U(1) 1-form symmetries.
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Generalized Families of QFTs
Generalized family anomalies for broken higher-group and non-invertible symmetries constrain RG flows and IR phases of QFT families, with explicit application to deformed 4d QCD.
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The Line, the Strip and the Duality Defect
The XY-plaquette model is claimed to possess a continuous SO(2) non-invertible duality symmetry at arbitrary coupling, realized by open condensation defects in its symmetry TFT.
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Non-invertible symmetries in the axiverse, and the imaginary wormholes
Imaginary wormholes and the IDB imply that towers of BPS EFT instantons generate infinitely many superpotential terms that break non-invertible axion shift symmetries in N=1 axiverse models.
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Notes on (-2)-form symmetries
Introduces (-2)-form symmetries that modify the SymTFT action to relate QFTs differing by anomaly data or non-invertible symmetry associators, illustrated in 2D-4D models, fusion categories, club-sandwich RG flows, an...
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SymTFT for Continuous Symmetries: Non-linear Realizations and Spontaneous Breaking
Continuous-symmetry SymTFTs are extended to non-linear coset realizations and to spontaneous breaking using boundary and corner constructions, recovering CCWZ actions and SSB Ward identities.
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SymTFT actions, Condensable algebras and Categorical anomaly resolutions
For Q8 and Rep(Q8), the paper computes condensable algebras, identifies intrinsically gapless SPT phases, and derives fusion-category short exact sequences that resolve categorical anomalies.
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Is Crane--Yetter fully extended?
Fully extended invertible 4D TQFTs valued in braided fusion categories form a Z/6-extension of the Witt group, so Crane-Yetter has six inequivalent point-refinements for fixed modular data.
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