Year: 2026
Type: preprint
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 $L^p$-bounded Higgs fields. Away from a singular set of codimension at least 4 and after suitable bundle identifications, the sequence subconverges in the $C^\infty_{\operatorname{loc}}$-topology.
Source: arXiv (Cornell University)
Author: Delgado, Jonathan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7221809942