On 2-group global symmetries and their anomalies

By F. Benini, Clay Córdova, Po-Shen Hsin. Journal of High Energy Physics, 2018

258 citations recorded by the source corpus.

A bstractIn general quantum field theories (QFTs), ordinary (0-form) global symmetries and 1-form symmetries can combine into 2-group global symmetries. We describe this phenomenon in detail using the language of symmetry defects. We exhibit a simple procedure to determine the (possible) 2-group global symmetry of a given QFT, and provide a classification of the related ’t Hooft anomalies (for symmetries not acting on spacetime). We also describe how QFTs can be coupled to extrinsic backgrounds for symmetry groups that differ from the intrinsic symmetry acting faithfully on the theory. Finally, we provide a variety of examples, ranging from TQFTs (gapped systems) to gapless QFTs. Along the way, we stress that the “obstruction to symmetry fractionalization” discussed in some condensed matter literature is really an instance of 2-group global symmetry.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cc019bea43a05e611f0a48b0e906c97357cf8d63

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Citations in the corpus

Anomalies in the space of coupling constants and their dynamical applications II (2019, background): “25 This means that the mixed anomaly between the periodicity of θ and the one-form ZN global symmetry is cancelled at the cost of making the background field B participate together with A in a higher group structure [59–61].”
Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond (2022, background): “This includes results for familiar continuous global symmetries [214–220], discrete global symmetries [221–225,56,226–230], higher-form and higher-group symmetries [52,54,58,59,231,74], and subsystem symmetries [144, 147, 148], families of quantum field theories [232–241], as well as structural deve”
Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions (2022, background): “2) form a natural component of the algebraic structure of a higher fusion category [52–62], generalizing the simpler higher algebraic structures defining higher-form and higher group global symmetry [1, 63, 64].”
On gauging finite subgroups (2017, background): “These issues are treated in detail from the physics point of view in a paper by Benini, Córdova and Hsin [32].”
Generalized Symmetries in Condensed Matter (2022, unknown): “Though it has not yet explicitly played a role in the condensed matter literature to my knowledge, it appears in many places in QFT ( e.g. (137, 138, 104, 139)) and we can expect that it will be useful.”
Exploring 2-group global symmetries (2018, background): “up symmetry of the GM model is essential to making its ’t Hooft anomalies compatible with anomaly in ow from a ve-dimensional bulk. 26 of these, and other, aspects of discrete 2-groups will appear in [32]. Finally, we would like to point out that some of the phenomena described in [33{35], which als”
Universal Non‐Invertible Symmetries (2022, background): “The split/non-split distinction is characterized by the triviality/non-triviality of the Postnikov class which is an element in the ρ- twisted group cohomology ω ∈ H(3) ρ(Γ , Γ((1))) [14, 15].”
Dai-Freed anomalies in particle physics (2018, background): “See [26] for more examples of TQFTs with the same anomaly as local quantum field theories of interest, also applying to generalized global symmetries.”
Comments on one-form global symmetries and their gauging in 3d and 4d (2018, background): “the line and it implies that if we view this line as the worldline of a probe particle, this particle is a fermion [39, 44].”