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Fermionic Bogomolnyi-Prasad-Sommerfield Wilson loops in four-dimensional $\mathcal{N}=2$ superconformal gauge theories

by Hao Ouyang, Jun-Bao Wu

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Submission summary

Authors (as registered SciPost users): Hao Ouyang · Jun-Bao Wu
Submission information
Preprint Link:  (pdf)
Date accepted: 2022-10-06
Date submitted: 2022-09-20 02:50
Submitted by: Wu, Jun-Bao
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


We construct for the first time Drukker-Trancanelli (DT) type fermionic Bogomol\`nyi-Prasad-Sommerfield (BPS) Wilson loops in four-dimensional $\mathcal{N}=2$ superconformal $SU(N)\times SU(N)$ quiver theory and $\mathcal{N}=4$ super Yang-Mills theory. The connections of these fermionic BPS Wilson loops have a supermatrix structure. We construct timelike BPS Wilson lines in Minkowski spacetime and circular BPS Wilson loops in Euclidean space. These Wilson loops involve dimensionful parameters. For generic values of parameters, they preserve one real (complex) supercharge in Lorentzian (Euclidean) signature. Supersymmetry enhancement for Wilson loops happens when the parameters satisfy certain constraints. The nature of such loops is quite different from the Wilson loop operators involving fermions constructed previously in the literature on four-dimensional gauge theories. We hope that further investigations of such new Wilson loops will explore deep structures in both the gauge theories and gauge/gravity dualities.

Author comments upon resubmission

Dear Editors,

Let us thank the referees for their careful reading of the manuscript and valuable comments. We resubmit a modified version of our manuscript after making the changes suggested. We have attached the replies to issues raised by the referees and corresponding changes below.

Sincerely yours,

Hao Ouyang and Jun-Bao Wu

List of changes

Reply to Anonymous Report 1:

We thank the referee very much for his/her valuable comments. We address the requests:

1) We added a paragraph at the end of section 4 to discuss the consequences of the dimensionful couplings.

2) We added a comment about the framing issue at the end of the second paragraph in section 4 which is related to the perturbative computation of the WL vev.

3) We gave the first few order result of V in Eq (53). The complete construction of $V$ can be performed following the procedure in appendix D of 1506.06192.

Reply to Anonymous Report 2:

We thank the referee for his/her report and careful reading of our manuscript.

1) We thank the referee for pointing out many typos, which we have corrected in the revised version.

2) We added a paragraph on page 3 and a footnote on page 4 to address the referee's comments on our introduction. We also added a paragraph on page 4 to stress that this is the first construction of Drukker-Trancanelli type fermionic BPS
Wilson loops in 4d.

3) We added a sentence above (48) to mention how the G_s^2
piece is obtained in section 2.3.

4) The number of preserved supercharges is equal to the number of free parameters in u_\alpha. In another word, it is just the dimension of the linear space of the preserved supercharges. Detailed clarifications were added on page 12.

5) It should be QF above (44), as pointed out by the referee.

6) We added a paragraph at the end of section 4 to discuss the consequences of scale invariance breaking due to fermions in the WL.

7) We changed the order of B.1 and B.2.

Published as SciPost Phys. 14, 008 (2023)

Reports on this Submission

Anonymous Report 1 on 2022-10-2 (Invited Report)


The authors have addressed my comments and I think the
paper is now much improved. I think it can be published.

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

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Anonymous on 2022-09-22  [id 2843]


The authors have successfully addressed my comments in this revised version. In my opinion, the manuscript is now ready to be published.