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Chiral Gauge Theories on $R^3 \times S^1$ and SUSY Breaking

by Jun Seok Lee, John Terning

Submission summary

As Contributors: Jun Seok Lee · John Terning
Arxiv Link: (pdf)
Date submitted: 2019-09-20 02:00
Submitted by: Terning, John
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
  • High-Energy Physics - Phenomenology
Approach: Theoretical


We study SU(5) chiral gauge theories on $R^3\times S^1$. With an unequal number of fundamental and antifundmental matter representations we calculate nontrivial pre-ADS superpotentials generated by composite multi-monopoles. We also point out that the structure of the composite multi-monopoles can be determined simply from the affine Dynkin diagrams of the gauge group and its unbroken subgroup. For the case of one flavor, we find that the superpotential is independent of the composite meson. We show that dynamical 4D SUSY breaking in the simplest chiral SU(5) gauge theory can be demonstrated directly via semi-classical effects on the circle.

Current status:
Editor-in-charge assigned

Submission & Refereeing History

Reports on this Submission

Anonymous Report 2 on 2019-10-23 (Invited Report)


1 - Nice analysis of a class of SUSY gauge theories compactified on a circle.

2 - Nice discussion of monopole effects in these theories.


No real weaknesses, except that more motivation for this analysis would be nice to see in the introduction.


This paper presents a thorough analysis of monopole effects and their relation to SUSY breaking in SU(5) ${\cal N}=1$ SYM theories with antisymmetric tensor, fundamental and antifundamental matter chiral multiplets. By compactifying one dimension on a circle, the authors are able to interpolate between results in 3D and 4D. Some of the other usual techniques of interpolating between theories are employed, for example by integrating out flavors. Where independent analyses are available, the authors compare their results with the existing literature.

One nice feature of the manuscript is the appendices, where details of some of the hard labor appears, including analysis of zero modes on monopole configurations and exploration of the different regions in the moduli space of these theories.

In my opinion this is a fine analysis of a class of SUSY gauge theories, and while the phenomenological motivation for such analyses is becoming less obvious with time, this work is a worthy addition to the literature.

Requested changes

I really have only one minor suggestion and two questions that the authors might consider responding to by adding a sentence or two to the text.

1- Unless I missed it, the notation for Coulomb branch operators in the effective superpotentials of Table 2 are not explained until much later in the text and appendices. It would be helpful either to provide brief definitions of notation in either the caption to Table 2 or the surrounding text, or else to point to the relevant places elsewhere in the text where the notation is subsequently defined.

2 - For my own edification, as part of the discussion of the interpolation between the compactified and uncompactified theories, I would have appreciated some additional comments regarding which, if any, topological effects might persist in the decompactified limit.

3 - Even if the objective importance of dynamical SUSY breaking and monopole confinement is self-evident, a gesture to possible phenomenological applications of these models or techniques would be nice to see.

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

Anonymous Report 1 on 2019-9-30 (Invited Report)


This is a nice paper presenting a detailed analysis of the dynamics of a chiral SU(5) theory compactified on the circle. It lends further support to both known ADS superpotentials in 4d and to pre-ADS superpotential in the circle-compactified theory. Further, there is new evidence in favor of the supersymmetry-breaking scenario of the one-flavor SU(5) theory.


The only weakness I can think of is the very technical nature of the subject. I am not sure it can be remedied, it certainly requires familiarity/reading of previous papers (incl. ones by the authors). I do not hold this remark against the paper.


I recommend this paper for publication. The main reason is the new essentially semiclassical argument for supersymmetry breaking in the F=0 theory presented in the paper.

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

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