Higher Symmetries of 5d Orbifold SCFTs

TL;DR

This paper characterizes the higher symmetries of 5d SCFTs from M-theory on complex orbifold backgrounds, providing methods to extract symmetry data even in non-toric or non-isolated singularities, and clarifies their intrinsic nature.

Contribution

It introduces two independent methods to determine higher symmetries of 5d SCFTs from orbifold singularities, applicable to non-abelian and non-isolated cases, confirming their intrinsic nature.

Findings

Higher symmetries are determined by BPS states encoded in quiver quantum mechanics.

The same symmetry data can be obtained via defect group computations, independent of resolutions.

The abelianization of the orbifold group reveals 2-group structures when the geometry captures the global symmetry.

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.