Higher Symmetries of 5d Orbifold SCFTs

Abstract

We determine the higher symmetries of 5d SCFTs engineered from M-theory on a ${\mathbb{C}}^3/\Gamma$ background for $\Gamma$ a finite subgroup of $SU(3)$. This resolves a longstanding question as to how to extract this data when the resulting singularity is non-toric (when $\Gamma$ is non-abelian) and/or not isolated (when the action of $\Gamma$ has fixed loci). The BPS states of the theory are encoded in a 1d quiver quantum mechanics gauge theory which determines the possible 1-form and 2-form symmetries. We also show that this same data can also be extracted by a direct computation of the corresponding defect group associated with the orbifold singularity. Both methods agree, and these computations do not rely on the existence of a resolution of the singularity. We also observe that when the geometry faithfully captures the global 0-form symmetry, the abelianization of $\Gamma$ detects a 2-group structure (when present). As such, this establishes that all of this data is indeed intrinsic to the superconformal fixed point rather than being an emergent property of an IR gauge theory phase.

v2: 42 pages, 5 figures, reference added, typos corrected, clarifications added

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Cited by in corpus (13)

• Non-Invertible Higher-Categorical Symmetries
• Non-invertible Symmetries of Class $\mathcal{S}$ Theories
• Symmetry TFTs for 3d QFTs from M-theory
• 2-Group Symmetries and M-Theory
• 0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds
• Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices
• Anomalies of Generalized Symmetries from Solitonic Defects
• Disconnected 0-Form and 2-Group Symmetries
• 5d Higgs Branches from M-theory on quasi-homogeneous cDV threefold singularities
• A tale of 2-groups: D${}_p$(USp(2N)) theories
• Generalized Toric Polygons, T-branes, and 5d SCFTs
• Generalized Symmetries of Non-SUSY and Discrete Torsion String Backgrounds
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories