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Potency of nilpotence

Eric Bryan ^*, Arvind Rajaraman ^†, and Yuri Shirman ^‡

Department of Physics and Astronomy, University of California, Irvine, California 92697-4575, USA

^*Contact author: ebryan2@uci.edu
^†Contact author: arajaram@uci.edu
^‡Contact author: yshirman@uci.edu

Phys. Rev. D 113, 065022 – Published 25 March, 2026

DOI: https://doi.org/10.1103/xqkw-yz61

Abstract

The dynamics of $N = 1$ supersymmetric gauge theories with matter in adjoint and fundamental representations and the superpotentials given by Arnold’s ADE singularities has been extensively studied in the literature. It was also conjectured that supersymmetric models with $W_{A_{k}}$ , $W_{D_{k + 2}}$ , and $W_{E_{7}}$ superpotentials possess a dual description. In this paper, we revisit the analysis of the moduli space of $A_{k}$ and $D_{k + 2}$ models by considering the duality along nilpotent directions on the moduli space. While our analysis provides additional evidence for the duality conjecture in $W_{A_{k}}$ models, we show that the duality conjecture fails for the $W_{D_{k + 2}}$ models.

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Phys. Rev. D 113, 065022– Published 25 March, 2026

Vol. 113, Iss. 6 — 15 March 2026

Received 6 January 2026
Accepted 25 February 2026

DOI: https://doi.org/10.1103/xqkw-yz61

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physical Review D

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Potency of nilpotence

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References (15)

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