The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs

TL;DR

The paper establishes that certain 5d SCFTs possess 2-group symmetries formed by mixing 0-form flavor groups with 1-form symmetries, with the Postnikov class governing the extension. It develops a Geometry–Structure Group framework to extract the global form of flavor groups and the corresponding 2-group data directly from M-theory realizations, applying it to a broad class of theories including rank-1 Seiberg theories and higher-rank examples. The results include explicit flavor-group determinations (often center-reduced forms) and criteria for when a non-trivial 2-group arises, supported by checks against the superconformal and ray indices and by analyses of mixed anomalies and Higgs-branch matching. Circle-compactification to 4d and brane-web perspectives corroborate the 2-group structures and illuminate their perturbative and instantonic origins, offering a comprehensive view of how higher-form symmetries shape the global symmetry structure of 5d SCFTs.

Abstract

2-group symmetries arise when 1-form symmetries and 0-form symmetries of a theory mix with each other under group multiplication. We discover the existence of 2-group symmetries in 5d N=1 abelian gauge theories arising on the (non-extended) Coulomb branch of 5d superconformal field theories (SCFTs), leading us to argue that the UV 5d SCFT itself admits a 2-group symmetry. Furthermore, our analysis determines the global forms of the 0-form flavor symmetry groups of 5d SCFTs, irrespective of whether or not the 5d SCFT admits a 1-form symmetry. As a concrete application of our method, we analyze 2-group symmetries of all 5d SCFTs, which reduce in the IR, after performing mass deformations, to 5d N=1 non-abelian gauge theories with simple, simply connected gauge groups. For rank-1 Seiberg theories, we check that our predictions for the flavor symmetry groups match with the superconformal and ray indices available in the literature. We also comment on the mixed 't Hooft anomaly between 1-form and 0-form symmetries arising in 5d N=1 non-abelian gauge theories and its relation to the 2-groups.