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 obtain a family of ``effective cone Yang-Mills functionals''on the space of connection 1-forms indexed by $\zeta$, which reduce to Yang-Mills theory when $\zeta = 0$. 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 $t\zeta$-cone Yang-Mills equations.
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 alw...
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 study the $SU(2)$ Einstein-Yang-Mills system with non-minimal $RF^2$-type couplings of Yang-Mills fields to curvature, formulated with exterior differential forms and a Lagrange-multiplier constraint for the Levi-Civita connection. We show that the conformally flat Bertotti-Robinson geometry $AdS_2\times S^2$ carrie...
We provide the first mathematical construction of the non-Abelian Yang-Mills-Higgs measure on a two-dimensional torus by implementing Parisi and Wu's ``stochastic quantisation''procedure. We use a specific gauge covariant (but non-Markovian) approximation to the previously constructed associated Langevin dynamics and d...
Bjoern Bringmann, Sky Cao, M. Hairer et al.· 0 citations
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...
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
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