Related papers: Local monotonicity for the Yang-Mills-Higgs flow

A generalization of the two-dimensional Yang-Mills and generalized Yang-Mills theory is introduced in which the building B-F theory is nonlocal in the auxiliary field. The classical and quantum properties of this nonlocal generalization are…

Ensembles of magnetic defects represent quantum variables that have been detected and extensively explored in lattice ${\rm SU}(N)$ pure Yang-Mills theory. They successfully explain many properties of confinement and are strongly believed…

We propose and prove a new formula for the one-loop all same helicity Yang-Mills amplitudes. These amplitudes are seen to arise as a sum of products of two tree-level Berends-Giele currents connected by an effective propagator. To make…

It is shown that the beta functions for four dimensional N=2 supersymmetric Yang-Mills theory without matter give integral curves on the moduli space some of which are geodesics of the natural metric on the moduli space. In particular the…

We twist the monopole equations of Seiberg and Witten and show how these equations are realized in topological Yang-Mills theory. A Floer derivative and a Morse functional are found and are used to construct a unitary transformation between…

An explicit canonical transformation is constructed to relate the physical subspace of Yang-Mills theory to the phase space of the ADM variables of general relativity. This maps 3+1 dimensional Yang-Mills theory to local evolution of…

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…

We study the question of whether a sequence of non-instanton Yang-Mills connections can limit to a bubbling configuration composed only of instantons. In the case that the Uhlenbeck limit and the bubbles are of opposite charge, we determine…

We generalize our previous results (Theorem 1 and Corollary 2 in arXiv:1412.4114) and Theorem 1 in arXiv:1502.00668) on the existence of an $L^2$-energy gap for Yang-Mills connections over closed four-dimensional manifolds and energies near…

$F$-Yang-Mills connections are critical points of $F$-Yang Mills functional on the space of connections of a principal fiber bundle, which is a generalization of Yang-Mills connections, $p$-Yang-Mills connections and exponential Yang-Mills…

The Yang-Mills-Higgs equations (Y-M-H), when written relative to Lorenz gauge, become a system of nonlinear wave equations. The key bilinear terms in the resulting system turn out to be null forms--this is in light of a recent discovery of…

In this paper we study (static) solutions of the rank 2 Yang-Mills-Higgs equations on the Riemann sphere, with concical singularities, that bifurcate from constant curvature connections. We focus attention on the case where there are…

We develop a new method for proving regularity for small energy stationary solutions of coupled gauge field equations. Our results duplicate those of Tian--Tao [7] for the pure Yang Mills equations, but our proof is simpler, and obtains…

Exploiting the formulation of the Self Dual Yang-Mills equations as a Riemann-Hilbert factorization problem, we present a theory of pulling back soliton hierarchies to the Self Dual Yang-Mills equations. We show that for each map $ \C^4 \to…

We prove the existence of dark monopole solutions in a recently formulated Yang--Mills--Higgs theory model with technical features similar to the classical monopole problems. The solutions are obtained as energy-minimizing static…

The canonical formulation of general relativity is based on decomposition space--time manifold $M$ into $ R\times \Sigma$, this decomposition has to preserve the invariance of general relativity, invariance under general coordinates, and…

Given a $7$-dimensional compact Riemannian manifold $\left( M,g\right) $ that admits $G_{2}$-structure, all the $G_{2}$-structures that are compatible with the metric $g$ are parametrized by unit sections of an octonion bundle over $M$. We…

The classical Yang--Mills equations are analyzed within the geometrical framework of an effective gravity theory. Exact analytical solutions are derived for the cylindrically symmetric configurations of the coupled gauge and isoscalar…

In this paper, we use the affine Hermitian-Yang-Mills flow to prove a generalized Donaldson-Uhlenbeck-Yau theorem on flat Higgs bundles over a class of non-compact affine Gauduchon manifolds.

Some exact static solutions of the SU(2) Yang-Mills-Higgs theory are presented. These solutions satisfy the first order Bogomol'nyi equations, and possess infinite energies. They are axially symmetric and could possibly represent monopoles…