Eliminating the Higgs field and perturbing Yang-Mills connections in cone Yang-Mills theory
Abstract
We study the configurations of the cone Yang-Mills functional over a closed connected manifold. We show that the Euler-Lagrange equation from variations in the Higgs field is always uniquely solvable for ζ≠ 0, allowing us to eliminate one of the two equations from the theory. By eliminating the equation, we obtain a family of ``effective cone Yang-Mills functionals'' on the space of connection 1-forms indexed by ζ, which reduce to Yang-Mills theory when ζ= 0. This suggests a way to nontrivially deform the Yang-Mills moduli space. We take the first step towards this deformation by showing that, near certain critical points of the Yang-Mills functional, there is a family of smooth connections At which satisfy the tζ-cone Yang-Mills equations.
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BibTeX
@misc{delgado2026eliminating,
title = {{Eliminating the Higgs field and perturbing Yang-Mills connections in cone Yang-Mills theory}},
author = {Jonathan Delgado},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27734},
eprint = {2610.27734},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27734},
}
RIS
TY - UNPB
TI - Eliminating the Higgs field and perturbing Yang-Mills connections in cone Yang-Mills theory
AU - Jonathan Delgado
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27734
UR - https://arxiv.org/abs/2610.27734
AB - We study the configurations of the cone Yang-Mills functional over a closed connected manifold. We show that the Euler-Lagrange equation from variations in the Higgs field is always uniquely solvable for ζ≠ 0, allowing us to eliminate one of the two equations from the theory. By eliminating the equation, we obtain a family of ``effective cone Yang-Mills functionals'' on the space of connection 1-forms indexed by ζ, which reduce to Yang-Mills theory when ζ= 0. This suggests a way to nontrivially deform the Yang-Mills moduli space. We take the first step towards this deformation by showing that, near certain critical points of the Yang-Mills functional, there is a family of smooth connections A_t which satisfy the tζ-cone Yang-Mills equations.
ER -