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

TL;DR

This paper uncovers 2-group symmetries in 5d SCFTs, revealing how 0-form and 1-form symmetries combine, and determines the global flavor symmetry structures, with checks against known theories and indices.

Contribution

It demonstrates the existence of 2-group symmetries in 5d SCFTs and determines their global flavor symmetry groups, providing a new understanding of symmetry structures in these theories.

Findings

2-group symmetries exist in 5d N=1 abelian gauge theories.

Global forms of flavor symmetry groups are determined for 5d SCFTs.

Predictions match known results for rank-1 Seiberg theories.

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.