Compactness of Cone Yang-Mills Connections
Abstract
We consider the cone Yang-Mills functional recently introduced by Tseng and Zhou. This functional generalizes the Yang-Mills functional by coupling it to a closed 2-form which can represent a geometric structure of interest, e.g. a symplectic form or Ricci form. While the perspective of dimensional reduction is not always possible, we show that a cone Yang-Mills field is always locally the dimensional reduction of a pure Yang-Mills field. We then prove a monotonicity formula and use the dimensional reduction framework to prove an ε-regularity theorem in two ways. Finally, we prove a compactness theorem for sequences of cone Yang-Mills connections with bounded action and Lp-bounded Higgs fields. Away from a singular set of codimension at least 4 and after suitable bundle identifications, the sequence subconverges in the C∞loc-topology.
Related
- Eliminating the Higgs field and perturbing Yang-Mills connections in cone Yang-Mills theory
- Decay estimates for Yang-Mills connections and Yang-Mills-Higgs pairs in higher dimensions
- Algebraic limits of Hermitian-Yang-Mills connections on Kähler surfaces
- Nonclosure of stationary Yang-Mills connections under weak convergence
- Non-Hermitian Yang--Mills Connections with Vanishing Chern Classes
BibTeX
@misc{delgado2026compactness,
title = {{Compactness of Cone Yang-Mills Connections}},
author = {Jonathan Delgado},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17472},
eprint = {2610.17472},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17472},
}
RIS
TY - UNPB
TI - Compactness of Cone Yang-Mills Connections
AU - Jonathan Delgado
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17472
UR - https://arxiv.org/abs/2610.17472
AB - We consider the cone Yang-Mills functional recently introduced by Tseng and Zhou. This functional generalizes the Yang-Mills functional by coupling it to a closed 2-form which can represent a geometric structure of interest, e.g. a symplectic form or Ricci form. While the perspective of dimensional reduction is not always possible, we show that a cone Yang-Mills field is always locally the dimensional reduction of a pure Yang-Mills field. We then prove a monotonicity formula and use the dimensional reduction framework to prove an ε-regularity theorem in two ways. Finally, we prove a compactness theorem for sequences of cone Yang-Mills connections with bounded action and L^p-bounded Higgs fields. Away from a singular set of codimension at least 4 and after suitable bundle identifications, the sequence subconverges in the C^∞_loc-topology.
ER -