Global 4-group symmetry and 't Hooft anomalies in topological axion electrodynamics

Abstract

We study higher-form global symmetries and a higher-group structure of a low-energy limit of $(3+1)$-dimensional axion electrodynamics in a gapped phase described by a topological action. We argue that the higher-form symmetries should have a semi-strict 4-group (3-crossed module) structure by consistency conditions of couplings of the topological action to background gauge fields for the higher-form symmetries. We find possible 't Hooft anomalies for the 4-group global symmetry, and discuss physical consequences.

51 pages, 3 figures

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• Anomalies of Generalized Symmetries from Solitonic Defects
• Relations among topological solitons
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• Disconnected 0-Form and 2-Group Symmetries
• Fractionally Charged Particles at the Energy Frontier: The SM Gauge Group and One-Form Global Symmetry
• Higher-group structure in $2n$-dimensional axion-electrodynamics
• Higher-group structure in lattice Abelian gauge theory under instanton-sum modification
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• Higher-Matter and Landau-Ginzburg Theory of Higher-Group Symmetries
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