Discrete gauge anomalies revisited

Abstract

We revisit discrete gauge anomalies in chiral fermion theories in $3+1$ dimensions. We focus on the case that the full symmetry group of fermions is $\mathrm{Spin}(4)\times {\mathbb{Z}}_n$ or $(\mathrm{Spin}(4)\times {\mathbb{Z}}_{2m})/{\mathbb{Z}}_2$ with ${\mathbb{Z}}_2$ being the diagonal ${\mathbb{Z}}_2$ subgroup. The anomalies are determined by the consistency condition --- based on the Dai-Freed theorem --- of formulating a chiral fermion theory on a generic spacetime manifold with a structure associated with either one of the above symmetry groups and are represented by elements of some finite abelian groups. Accordingly, we give a reformulation of the anomaly cancellation conditions, and compare them with the previous result by Ibáñez and Ross. The role of symmetry extensions in discrete symmetry anomalies is clarified in a formal fashion. We also study gapped states of fermion with an anomalous global ${\mathbb{Z}}_n$ symmetry, and present a model for constructing these states in the framework of weak coupling.

33 pages, 2 figures

References in corpus (1)

• Dai-Freed anomalies in particle physics

Cited by in corpus (20)

• Dai-Freed anomalies in particle physics
• Adjoint QCD${}_4$, Deconfined Critical Phenomena, Symmetry-Enriched Topological Quantum Field Theory, and Higher Symmetry-Extension
• Symmetric Mass Generation
• Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
• Beyond Standard Models and Grand Unifications: Anomalies, Topological Terms, and Dynamical Constraints via Cobordisms
• Anomalies and Symmetry Fractionalization
• Anomalies of Duality Groups and Extended Conformal Manifolds
• Anomaly Constraints on Gapped Phases with Discrete Chiral Symmetry
• Anomalies of Non-Invertible Symmetries in (3+1)d
• The anomaly that was not meant IIB
• Gapped Chiral Fermions
• Cobordism and Deformation Class of the Standard Model
• Ultra Unification
• Anomaly and Cobordism Constraints Beyond the Standard Model: Topological Force
• Anomaly inflow and $p$-form gauge theories
• Outer Automorphism Anomalies
• Proton Stability: From the Standard Model to Beyond Grand Unification
• Anomaly and Cobordism Constraints Beyond Grand Unification: Energy Hierarchy
• Comments on the Atiyah-Patodi-Singer index theorem, domain wall, and Berry phase
• Boundary condition and reflection anomaly in $2+1$ dimensions