The Global Form of Flavor Symmetries and 2-Group Symmetries in 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 \mathcal{N}=1𝒩=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 \mathcal{N}=1𝒩=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 \mathcal{N}=1𝒩=1 non-abelian gauge theories and its relation to the 2-groupS.