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 $\epsilon$-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.
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 $\zeta \neq 0$, allowing us to eliminate one of the two equations from the theory. By eliminating the equation, we o...
We develop a parabolic formulation of the Uhlenbeck gauge fixing theorem and use it to prove the maximal existence of the Yang-Mills flow in vector bundles over compact $n$-dimensional Riemannian manifolds for $n \geq 4$. We apply Moser's iteration technique \cite{Mo1} to give a new proof of the bound of the curvature....
Jared Casey, Hoi-Chan Chak, Min-Chun Hong· 1 citation
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, p...
Lucio Vacchiano, G. Chirco, S. Pascazio et al.· 0 citations
We construct a sequence of stationary weak Yang-Mills connections on the trivial vector bundle $B^5\times\mathbb{R}^{15}$ with structure group $\operatorname{SO}(15)$ whose weak limit is a nonstationary weak Yang-Mills connection. Motivated by the stationarity question arising in Tian's work on Yang-Mills compactness,...
On a symplectic manifold, any differential two-form has a natural decomposition into two components: a primitive part and a non-primitive one. Applying this decomposition to the curvature two-form of a principal bundle over a symplectic manifold, we obtain a natural splitting of the Yang-Mills (YM) functional into two...
Jonathan Delgado, Li-Sheng Tseng, Jia-Wei Zhou· 1 citation
We construct Yang-Mills theories with projected curvature kinetic terms, developing their analogy with MacDowell-Mansouri gravity and their connection to nonlinear sigma models. We begin with models exhibiting explicit symmetry breaking and use them to motivate gauge-covariant Higgs extensions. For $SO(2n)$, an orthogo...
P. Alvarez· 0 citations
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