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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: 2023-08-03 06:37
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 1 on 2023-10-9 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2307.13724v2, delivered 2023-10-09, doi: 10.21468/SciPost.Report.7921


The paper studies supersymmetry-breaking deformations of five-dimensional superconformal field theories. Combining the analysis of the 5d prepotential of ref [30] with the methods developed in references [20] and [21], the authors are able to study numerous families of theories. Of particular interest is the case of Sp(N) SYM with an antisymmetric hyper, which has a known holographic dual [46]. The study of the deformation from field theory thus highlights the importance of the study of non-SUSY deformations in gravity.


Some presentation issues in the introduction and minor typos, but easily solvable with minor revisions.


The paper uses field-theoretic and geometric methods to investigate the existence of non-supersymmetric conformal field theories in five dimensions. This is argued via a chain of arguments: first one studies deformations of the SCFT leading to SYM phases, which are described by the prepotential. The authors stress the importance of integration constants in the prepotential, which represent Chern-Simons levels for background vector multiplets. When different deformations are related by a symmetry of the fixed point, the gauge theory phases are related as well, and are sometimes referred to as ``UV duals''. Focusing on these, the authors are able to fix the Chern-Simons levels for the background vector multiplets. One then deforms breaking supersymmetry and, in presence of a particular change of levels, argue in favour of the existence of a phase transitions and a non-supersymmetric fixed point, of which the authors study the stability as well.

The paper represents a significant contribution to the literature, and I would recommend it for publication after the authors address the minor revisions described below.

Requested changes

1) Presentation. One of the key concepts used in the paper is that of "UV duality". This is something of a misnomer, accepted because of its common usage in the literature. I believe that it should be emphasized in the introduction that "UV dualities" between apparently inequivalent gauge theories are simply due to related susy-preserving mass deformations. This point is already present in the article at p. 6, but to avoid imprecisions I believe that it would be better to bring this forward to the introduction, taking the place of the sentence about the "continuation past infinite coupling of the weakly coupled gauge theory description" (p. 1 and p. 3). The RG flow is unidirectional, and the "infinite coupling limit" is not a well-defined operation, as stressed, for instance in [1812.10451].

2) Typos and clarifications.
- p. 1 +4: Is there a reason why ref [46] is not grouped together with [4-6] in the introduction?
- p. 1 +14: that the global symmetry of $E_1$ is $SO(3)_I$ instead of $SU(2)_I$ was first suggested in [36]
- p. 1 +17 (and elsewhere): it should be "Cartan subgroup" rather than "Cartan"
- p. 1 -17: I believe that the sentence would be clearer as "is however related to the original weakly coupled description by"
- p. 2 +2: "on a generic" $\to$ "at a generic"
- p. 2 -2: "the background CS levels for the instantonic symmetry"
- p. 6 - 18: Could the authors please clarify, perhaps in a footnote, what they mean by a "non-perturbative hypermultiplet"?
- p. 8 +5: "in terms"
- p. 9 +12: that the global symmetry of the fixed point of $SU(N)_N$ is $SO(3)_I$ instead of $SU(2)_I$ was first suggested in [31]
- p. 11 (33): I believe that it would be clearer if $\alpha$ was introduced in the text, e.g. "this integration constant $\alpha$ into the IMS prepotential"
- p. 12 +4: is there a proof of the fact that the Weyl group of the global symmetry of the SCFT should be S-duality in the $(p,q)$ web, apart from the fact that they have a related action? If not, perhaps "implemented" is too strong compared to "related"?
- p. 14 +4: "the gauginos being in the adjoint"
- p. 14 footnote 5: what group are the authors referring to? $d_{abc}$ for $SU(N)$ is not vanishing for $N\geq 3$.
- p. 15 - 3: "a shift of the CS level"
- p. 28 -8: "reach"
- p. 32 -8: I suppose that the authors here restricting to holographic supersymmetric fixed points?

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

Author:  Mohammad Akhond  on 2023-10-20  [id 4048]

(in reply to Report 1 on 2023-10-09)

We thank the referee for their comments on our paper. We have implemented all the changes requested. Please see below for detailed breakdown.

1) We have rephrased the paragraph in the opening page to stress the direction of the RG and clarify the precise meaning of UV-duality

2) The typos have been corrected as follows

  • P.1+4: References are now grouped together.
  • p. 1 +14: Indeed, we should have been more careful to give credit, the reference now appears in footnote 1
  • p. 1 +17 (and elsewhere): Fixed
  • p. 1 -17: We agree, we have modified this sentence accordingly
  • p. 2 +2: Fixed
  • p. 2 -2: Fixed
  • p. 6 - 18: Thanks for pointing out the lack of clarity. We added footnote 4 to explain.
  • p. 8 +5: Fixed
  • p. 9 +12: Reference added
  • p. 11 (33): We agree, thanks for your suggestion. We changed the sentence accordingly.
  • p. 12 +4: We are not aware of a rigorous proof, other than the observation that it works in most cases. We changed the sentence to reflect this.
  • p. 14 +4: Fixed
  • p. 14 footnote 5: We are referring to $d_{abc}$ in the adjoint representation. While for arbitrary irrep of SU(N) it is non-vanishing it vanishes for the adjoint. Point here being that integrating out the gauging (which is adjoint valued) does not modify the CS level for the gauge field. We modified the sentence to make this more clear.
  • p. 15 - 3: Fixed
  • p. 28 -8: Fixed
  • p. 32 -8: Indeed we are referring to holographic fixed points. We changed the wording in that sentence to reflect this more clearly

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