Related papers: A proof on energy gap for Yang-Mills connection

In this paper, we use the direct minimizing method to find Yang-Mills connections for $SO(3)$ bundles over closed four manifolds. By constructing test connections, we prove that a minimizing sequence converges strongly to a minimizer under…

Sengupta's lower bound for the Yang-Mills action on smooth connections on a bundle over a Riemann surface generalizes to the space of connections whose action is finite. In this larger space the inequality can always be saturated. The…

We apply our abstract gradient inequalities developed by the authors in arXiv:1510.03817 to prove Lojasiewicz--Simon gradient inequalities for the harmonic map energy function using Sobolev spaces which impose minimal regularity…

We lay the foundations of a Morse homology on the space of connections on a principal $G$-bundle over a compact manifold $Y$, based on a newly defined gauge-invariant functional $\mathcal J$. While the critical points of $\mathcal J$…

We study the moduli space of Yang--Mills connections on bundles over a conformally compact manifold $\overline{M}$. We prove that, for every Yang--Mills connection $A$ that satisfies an appropriate nondegeneracy condition, and for every…

We study the $L^2$ gradient flow of the Yang--Mills functional on the space of connection 1-forms on a principal $G$-bundle over the sphere $S^2$ from the perspective of Morse theory. The resulting Morse homology is compared to the heat…

In this paper, we prove a convergence theorem for sequences of Einstein Yang-Mills systems on $U(1) $-bundles over closed $n$-manifolds with some bounds for volumes, diameters, $L^{2}$-norms of bundle curvatures and $L^{\frac{n}{2}}$-norms…

We prove a sharp convergence theorem for the Yang-Mills flow on an $\mathrm{S}\mathrm{U}(r)$-bundle over a locally hyperK\"ahler ALE 4-manifold. Our main result is a noncompact version of the "parabolic gap theorem" previously established…

In this paper, we study the properties of the critical points of Yang-Mills-Higgs functional, which are called Yang-Mills-Higgs pairs. We first consider the properties of weakly stable Yang-Mills-Higgs pairs on a vector bundle over S^n (n >…

We construct Yang-Mills connections on SO(n)-bundles over spheres equipped with the Euclidean metric. We use a cohomogeneity one group action on the bundle to reduce the Yang-Mills-equation to a system of ordinary differential equations.…

We prove several abstract versions of the Lojasiewicz-Simon gradient inequality for an analytic functional on a Banach space that generalize previous abstract versions of this inequality, weakening their hypotheses and, in particular, the…

Given a principal bundle $P\to M$ over a Riemannian manifold with compact structure group $G$, let us consider a stationary Yang-Mills connection $A$ with energy $\int_M |F_A|^2\le \Lambda$. If we consider a sequence of such connections…

In this note we introduce a Yang-Mills bar equation on complex vector bundles over compact Hermitian manifolds as the Euler-Lagrange equation for a Yang-Mills bar functional. We show the existence of a non-trivial solution of this equation…

We prove that in the limit of the coupling going to infinity a Yang-Mills theory is equivalent to a $\lambda\phi^4$ theory with the dynamics ruled just by a homogeneous equation. This gives explicitly the Green function and the mass…

Given a bundle gerbe with connection on an oriented Riemannian manifold of dimension at least equal to 3, we formulate and study the associated Yang-Mills equations. When the Riemannian manifold is compact and oriented, we prove the…

A recent paper (arxiv.org:1810.00025) studied properties of a compactification of the moduli space of irreducible Hermitian-Yang-Mills connections on a hermitian bundle over a projective algebraic manifold. In this follow-up note, we show…

We consider the Abelian Yang-Mills-Higgs functional, in the non-self dual scaling, on a complex line bundle over a closed Riemannian manifold of dimension $n\geq 3$. This functional is the natural generalisation of the Ginzburg-Landau model…

The symplectic vortex equations admit a variational description as global minimum of the Yang-Mills-Higgs functional. We study its negative gradient flow on holomorphic pairs $(A,u)$ where $A$ is a connection on a principal $G$-bundle $P$…

A non-perturbative quantization of the Yang-Mills energy-mass functional with a compact semi-simple gauge group entails an infinite discrete energy-mass spectrum of gauge bosons. The bosonic spectrum is bounded from below, and has a…

We consider the reduced Hamiltonian of the Yang-Mills field on $\mathbb{R}^4$ equipped with a Lorentzian metric. We show that the secondary quantized principal term $H_0$ of the Taylor expansion of this Hamiltonian at the lowest energy…