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Main Authors: Chakraborty, Mrigankamauli, Moch, Sven-Olaf
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2603.02892
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author Chakraborty, Mrigankamauli
Moch, Sven-Olaf
author_facet Chakraborty, Mrigankamauli
Moch, Sven-Olaf
contents 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 $\mathcal{N}=2$ 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 $\mathcal{N}=4$ SYM only at five loops, consistent with existing four-loop results. Our findings confirm that DR preserves supersymmetry for $\mathcal{N}=1, 2$ and $4$ SYM through the loop orders examined.
format Preprint
id arxiv_https___arxiv_org_abs_2603_02892
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Dimensional Reduction is Supersymmetric at Three Loops
Chakraborty, Mrigankamauli
Moch, Sven-Olaf
High Energy Physics - Theory
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 $\mathcal{N}=2$ 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 $\mathcal{N}=4$ SYM only at five loops, consistent with existing four-loop results. Our findings confirm that DR preserves supersymmetry for $\mathcal{N}=1, 2$ and $4$ SYM through the loop orders examined.
title Dimensional Reduction is Supersymmetric at Three Loops
topic High Energy Physics - Theory
url https://arxiv.org/abs/2603.02892