Anomalies of discrete symmetries in three dimensions and group cohomology

2014/03/03 by Anton Kapustin, Ryan Thorngren · 1 voice · 7 citations
Physics and Astronomy · #Noncommutative and Quantum Gravity Theories #Physics of Superconductivity and Magnetism #Topological Materials and Phenomena #cond-mat.str-el #hep-th

paper · pdf · doi:10.1103/physrevlett.112.231602

published as Phys. Rev. Lett. 112, 231602 (2014) · 4 pages, latex

arxiv created 2014/03/03 · openalex publication_date 2014/06/13 · arxiv updated 2014/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study 't Hooft anomalies for a global discrete internal symmetry G. We construct examples of bosonic field theories in three dimensions with a non-vanishing 't Hooft anomaly for a discrete global symmetry. We also construct field theories in three dimensions with a global discrete internal symmetry G₁ x G₂ such that gauging G₁ necessarily breaks G₂ and vice versa. This is analogous to the Adler-Bell-Jackiw axial anomaly in four dimensions and parity anomaly in three dimensions.

Citations

• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• Axial-Vector Vertex in Spinor Electrodynamics

Cited by

• Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond
• Construction of bosonic symmetry-protected-trivial states and their topological invariants viaG×SO(∞)nonlinearσmodels
• Anomaly constraint on chiral central charge of (2+1)d topological order
• Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators
• Intrinsically gapless topological phases
• Anomaly indicators and bulk-boundary correspondences for three-dimensional interacting topological crystalline phases with mirror and continuous symmetries
• High-temperature domain walls of QCD with imaginary chemical potentials

Discussions

• The most clear answer is probably found in this paper by Xiao-Gang Wen. It is important to note that the "anomalies" present in the discussion are 't Hooft anomalies. These anomalies appear when one h [stackexchange, 0 points]

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• Anomalies of discrete symmetries in various dimensions and group cohomology
• 't Hooft anomalies of discrete gauge theories and non-abelian group cohomology
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• Anomaly of Continuous Symmetries from Topological Defect Network