Anomalies of discrete symmetries in various dimensions and group cohomology

Abstract

We study 't Hooft anomalies for discrete global symmetries in bosonic theories in 2, 3 and 4 dimensions. We show that such anomalies may arise in gauge theories with topological terms in the action, if the total symmetry group is a nontrivial extension of the global symmetry by the gauge symmetry. Sometimes the 't Hooft anomaly for a d-dimensional theory with a global symmetry G can be canceled by anomaly inflow from a (d+1)-dimensional topological gauge theory with gauge group G. Such d-dimensional theories can live on the surfaces of Symmetry Protected Topological Phases. We also give examples of theories with more severe 't Hooft anomalies which cannot be canceled in this way.

31 pages, latex. v2: introduction expanded, references added, typos corrected

References in corpus (4)

• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
• Anomalies of discrete symmetries in three dimensions and group cohomology
• Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases

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