Gauge-covariant Hadamard descent in Yang-Mills theory
Abstract
We study the dimensional reduction of non-Abelian Yang-Mills theory from five to four dimensions. In this framework, Hadamard descent is formulated as a restriction to gauge-equivalence classes that are invariant, up to gauge transformations, under translations along the reduced direction. The central result is that, prior to gauge fixing, the adjoint scalar of the reduced theory is not the connection component Au itself, but the gauge-covariant combination Φ̃=ε−ιYA, which follows naturally from the covariant Cartan identity. The usual identification with Au is recovered, up to the sign convention adopted here, in the u-independent gauge, while global holonomy data remain additional information to be specified separately. We show that the reduced theory takes the form of a Yang--Mills--Higgs theory with the Higgs field in the adjoint representation. As an example, we focus on the U(2) gauge theory and analyze the Higgs mechanism, together with the associated symmetry breaking pattern, when the reduced theory is expanded around the ground state of the parent theory. We then include fermions and show that, in the u-independent gauge, the extra-dimensional component of the gauge connection generates a pseudoscalar Yukawa coupling which, on the vacuum configuration, can be converted into a fermion mass term by a chiral field redefinition, while the gauge interaction remains vectorial.
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BibTeX
@misc{vacchiano2026gaugecovariant,
title = {{Gauge-covariant Hadamard descent in Yang-Mills theory}},
author = {Lucio Vacchiano and Goffredo Chirco and Saverio Pascazio and Patrizia Vitale},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08515},
eprint = {2610.08515},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08515},
}
RIS
TY - UNPB
TI - Gauge-covariant Hadamard descent in Yang-Mills theory
AU - Lucio Vacchiano
AU - Goffredo Chirco
AU - Saverio Pascazio
AU - Patrizia Vitale
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08515
UR - https://arxiv.org/abs/2610.08515
AB - We study the dimensional reduction of non-Abelian Yang-Mills theory from five to four dimensions. In this framework, Hadamard descent is formulated as a restriction to gauge-equivalence classes that are invariant, up to gauge transformations, under translations along the reduced direction. The central result is that, prior to gauge fixing, the adjoint scalar of the reduced theory is not the connection component A_u itself, but the gauge-covariant combination Φ̃=ε−ι_YA, which follows naturally from the covariant Cartan identity. The usual identification with A_u is recovered, up to the sign convention adopted here, in the u-independent gauge, while global holonomy data remain additional information to be specified separately. We show that the reduced theory takes the form of a Yang--Mills--Higgs theory with the Higgs field in the adjoint representation. As an example, we focus on the U(2) gauge theory and analyze the Higgs mechanism, together with the associated symmetry breaking pattern, when the reduced theory is expanded around the ground state of the parent theory. We then include fermions and show that, in the u-independent gauge, the extra-dimensional component of the gauge connection generates a pseudoscalar Yukawa coupling which, on the vacuum configuration, can be converted into a fermion mass term by a chiral field redefinition, while the gauge interaction remains vectorial.
ER -