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't Hooft lines of ADE-type and Topological Quivers

by Youssra Boujakhrout, El Hassan Saidi, Rachid Ahl Laamara, Lalla Btissam Drissi

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Submission summary

Authors (as registered SciPost users): Youssra Boujakhrout
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-05-31
Date submitted: 2023-03-27 09:02
Submitted by: Boujakhrout, Youssra
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


We investigate 4D Chern-Simons theory with ADE gauge symmetries in the presence of interacting Wilson and 't Hooft line defects. We analyse the intrinsic properties of these lines' coupling and explicate the building of oscillator-type Lax matrices verifying the RLL integrability equation. We propose gauge quiver diagrams Q$_{G}^{\mu }$ encoding the topological data carried by the Lax operators and give several examples where Darboux coordinates are interpreted in terms of topological bi-fundamental matter. We exploit this graphical description $\left( i\right) $ to give new results regarding solutions in representations beyond the fundamentals of $sl_{N}$, $% so_{2N}$ and $e_{6,7}$, and $\left( ii\right) $ to classify the Lax operators for simply laced symmetries in a unified E$_{7}$ CS theory. For quick access, a summary list of the leading topological quivers Q$% _{ADE}^{\mu }$ is given in the conclusion section [Figures 29.(a-e), 30.(a-d) and 31.(a-d)].

Author comments upon resubmission

Enclosed is the second version of the manuscript.

List of changes

Modifications following questions of Referee 1 are included in the new verion as detailed in the report's answer. In particular, an appendix is added (page68) and Section 3.1 (page 18) is reformulated.
Rectifications recommended by Referee 2 are also inserted; typographical errors are corrected.

Published as SciPost Phys. 15, 078 (2023)

Reports on this Submission

Anonymous Report 1 on 2023-4-18 (Invited Report)


The suggested in the original report have been implemented by the authors. All looks good.

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