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5d SCFTs and their non-supersymmetric cousins

by Mohammad Akhond, Masazumi Honda, Francesco Mignosa

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Submission summary

Authors (as registered SciPost users): Mohammad Akhond
Submission information
Preprint Link:  (pdf)
Date submitted: 2023-10-20 07:23
Submitted by: Akhond, Mohammad
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


We consider generalisations of the recently proposed supersymmetry breaking deformation of the 5d rank-1 $E_1$ superconformal field theory to higher rank. We generalise the arguments to theories which admit a mass deformation leading to gauge theories coupled to matter hypermultiplets at low energies. These theories have a richer space of non-supersymmetric deformations, due to the existence of a larger global symmetry. We show that there is a one-to-one correspondence between the non-SUSY deformations of the gauge theory and their $(p,q)$ 5-brane web. We comment on the (in)stability of these deformations both from the gauge theory and the 5-brane web point of view. UV duality plays a key role in our analysis, fixing the effective Chern-Simons level for the background vector multiplets, together with their complete prepotential. We partially classify super-Yang-Mills theories known to enjoy UV dualities which show a phase transition where different phases are separated by a jump of Chern-Simons levels of both a perturbative and an instantonic global symmetry. When this transition can be reached by turning on a non-supersymmetric deformation of the UV superconformal field theory, it can be a good candidate to host a 5d non-supersymmetric CFT. We also discuss consistency of the proposed phase diagram with the 't Hooft anomalies of the models that we analyse.

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 2 on 2023-12-2 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2307.13724v4, delivered 2023-12-02, doi: 10.21468/SciPost.Report.8213


This paper analyzes whether non-supersymmetric deformations of five-dimensional superconformal field theories with a rank greater than one can give rise to an interacting 5D fixed point without supersymmetry. This generalizes previous results obtained in the rank-one case. The use of $(p,q)$-fivebrane webs plays a prominent role in this analysis.


Understanding the dynamics of 5D SCFTs and their non-supersymmetric deformations is a challenging task. The $(p,q)$-brane webs approach certainly offers useful consistency checks, but it is not completely clear whether it can also provide definitive answers to the questions that the authors would like to address.

Section 2.2 has a a couple of presentation issues , but they can be easily resolved with some minor revisions.


The paper makes a worthy contribution to the existing literature on 5D SCFTs, and I recommend it for publication once the authors address the minor revisions outlined below.

Requested changes

1) On page 6, the authors refer to "non-perturbative hypermultiplets." Please see additional comments in Footnote 4. I suggest removing this terminology, the footnote and any subsequent references to it, as it holds little significance. Additionally, contrary to what is stated in Footnote 4, there is no QFT proof that 5D supersymmetric gauge theories or SCFTs exhibit S-duality.

2) Overall, Section 2.2 is unnecessarily verbose, containing numerous small subsections that could be easily integrated into a single section. To enhance the reader's experience, it would be beneficial if the authors could provide a more streamlined version of Section 2.2 upon resubmission.

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Author:  Mohammad Akhond  on 2023-12-25  [id 4210]

(in reply to Report 2 on 2023-12-02)

I wish to thank the referee for their comments.

1) All reference to non-perturbative hypermultiplets is now removed, instead we use the terminology non-perturbative states, which is more accurate. Note, that v6 is the latest draft, somehow I missed one such phrase in v5 which is resubmitted here.

2) This section has now been streamlined along the lines suggested by the referee.

Thanks again for your comments.

Anonymous Report 1 on 2023-10-23 (Invited Report)


I would like to thank the authors for answering my questions and implementing the changes.
I recommend the paper for publication.

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