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  • Open Access

Dimensional Reduction Is Supersymmetric at Three Loops

Mrigankamauli Chakraborty* and Sven-Olaf Moch†

  • II. Institute for Theoretical Physics, Universität Hamburg Luruper Chaussee 149, 22761 Hamburg, Germany

  • *Contact author: mrigankamauli.chakraborty@desy.de
  • †Contact author: sven-olaf.moch@desy.de
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Phys. Rev. Lett. 137, 191602 – Published 3 November, 2026

DOI: https://doi.org/10.1103/wqyz-ckqg

Abstract

We resolve the long-standing claim that regularization by dimensional reduction (DR) fails to preserve supersymmetry in supersymmetric Yang–Mills (SYM) theories at three loops. Earlier results reported a mismatch between the Yukawa and ghost-gluon β functions in N=2 SYM, suggesting a breakdown of supersymmetry. We show that this discrepancy does not originate from DR itself but from subtleties in the treatment of the Clifford algebra. A corrected three-loop calculation restores full supersymmetric behavior, and we demonstrate that the same issue would first affect N=4 SYM only at five loops, consistent with existing four-loop results. Our findings confirm that DR preserves supersymmetry for N=1, 2, and 4 SYM through the loop orders examined.

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Phys. Rev. Lett. 137, 191602– Published 3 November, 2026
  • Received 11 March 2026
  • Revised 30 July 2026
  • Accepted 6 October 2026
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