Wess–Zumino coupling of the compactified M2-brane forces its monopole 0-form and winding 1-form symmetries into a 2-group whose Postnikov class is the mixed quantized flux.
2-Group Symmetries and M-Theory
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abstract
Quantum Field Theories engineered in M-theory can have 2-group symmetries, mixing 0-form and 1-form symmetry backgrounds in non-trivial ways. In this paper we develop methods for determining the 2-group structure from the boundary geometry of the M-theory background. We illustrate these methods in the case of 5d theories arising from M-theory on ordinary and generalised toric Calabi-Yau cones, including cases in which the resulting theory is non-Lagrangian. Our results confirm and elucidate previous results on 2-groups from geometric engineering.
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2-Group global symmetry in the compactified M2-brane
Wess–Zumino coupling of the compactified M2-brane forces its monopole 0-form and winding 1-form symmetries into a 2-group whose Postnikov class is the mixed quantized flux.
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Generalised global symmetries in 5d $\mathcal{N}=1$ theories from the blow-up equations
Blow-up equation prefactors encode cubic 1-form self-anomalies and mixed anomalies of 5d N=1 SCFTs, deciding 2-group vs mixed anomaly structure.
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Quiver Approach to Symmetry Theories
An algebraic method using the path algebra of quivers extracts symmetry anomaly data for 5D SCFTs engineered from M-theory on Calabi-Yau cones.
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ICTP Lectures on (Non-)Invertible Generalized Symmetries
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Lectures on Generalized Symmetries
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.