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

by Fabio Apruzzi, Lakshya Bhardwaj, Jihwan Oh, Sakura Schafer-Nameki

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Submission summary

Authors (as registered SciPost users): Lakshya Bhardwaj
Submission information
Preprint Link:  (pdf)
Date accepted: 2022-07-05
Date submitted: 2022-02-24 17:30
Submitted by: Bhardwaj, Lakshya
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


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.

Published as SciPost Phys. 13, 024 (2022)

Reports on this Submission

Anonymous Report 2 on 2022-6-27 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2105.08724v3, delivered 2022-06-27, doi: 10.21468/SciPost.Report.5297


This paper studies 2-group global symmetries in 5D SCFT’s. The authors demonstrate that there is a general phenomenon that leads to 2-group global symmetries in 5D theories where there is a redundancy between the global and gauge symmetry of the theory. In this paper, the authors work in detail through an explicit example, demonstrating the existence of 2-group symmetries through multiple methods. The authors use this analysis to argue that the existence of 2-group global symmetries on the Coulomb branch of a SCFT must be matched by the UV theory. I highly recommend this paper for publication.

  • validity: high
  • significance: good
  • originality: high
  • clarity: high
  • formatting: excellent
  • grammar: perfect

Anonymous Report 1 on 2022-3-29 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2105.08724v3, delivered 2022-03-29, doi: 10.21468/SciPost.Report.4811


The manuscript studies the 2-group symmetries in various 5d SCFTs, and in particular the global form of the 0-form symmetry. The symmetries are determined from the low energy gauge theory on the Coulomb branch or after mass deformations. The symmetry is also verified using the known superconformal and ray indices.

The results are interesting and I recommend the manuscript for publication after following minor points are taken care of.
-p35. For option 1, is it clear that the anomaly (3.48) is well-defined for 2-group bundles where $B$ is not closed?
-p36. In (3.54), the cup1 product is not associative so the equation needs a bracket.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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