• Accepted Paper

Dimensional reduction is supersymmetric at three loops

Mrigankamauli Chakraborty and Sven-Olaf Moch

Phys. Rev. Lett. - Accepted 6 October, 2026

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

Abstract

We resolve the long-standing claim that regularisation by dimensional reduction (DR) fails to preserve supersymmetry in Super 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 supersymmertry. 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 behaviour, 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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