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

In this paper, we study the Yang-Mills functional on quantum Heisenberg manifolds using the appratuses developed by A. Connes and M. Rieffel. It is discovered that a connection on a projective module over a quantum Heisenberg manifold is a…

A local monotonicity formula for the Yang-Mills-Higgs flow on $G$-bundles over $\mathbb{R}^{n}$ ($n>4$) is proved. It is shown that the monotone quantity co\"incides on certain self-similar solutions with that appearing in existing…

Assuming that a non-trivial quantum Yang-Mills theory exists, we have proved that it should have a mass gap $\Delta^2 > 0$, indeed. The proof is based on the derivation of the novel constraint on any solution to QCD. It has been exactly and…

The purpose of this work is to present a Non--Commutative Geometrical version of the Yang--Mills Theory and the Yang--Mills Scalar Matter Theory by constructing a concrete example using M. Durdevich's theory of quantum principal bundles.

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…

We prove a conformally invariant estimate for the index of Schr\"odinger operators acting on vector bundles over four-manifolds, related to the classical Cwikel-Lieb-Rozenblum estimate. Applied to Yang-Mills connections we obtain a bound…

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…

In this paper, we define a family of functionals generalizing the Yang-Mills-Higgs functional on a closed Riemannian manifold. Then we prove the short time existence of the corresponding gradient flow by a gauge fixing technique. The lack…

In this work, along with the companion work Oh (2012), we propose a novel approach to the problem of gauge choice for the \emph{Yang-Mills equations} on the Minkowski space $\mathbb{R}^{1+3}$. A crucial ingredient is the associated…

Let A be the space of irreducible connections (vector potentials) over a SU(n)-principal bundle on a three-dimensional manifold M. Let T be the fiber product of the tangent and cotangent bundles of A. We endow T with a symplectic structure…

Yang-Mills theory is growing at the interface between high energy physics and mathematics. It is well known that Yang-Mills theory and Gauge theory in general had a profound impact on the development of modern differential and algebraic…

We consider Lie(G)-valued G-invariant connections on bundles over spaces G/H, RxG/H and R^2xG/H, where G/H is a compact nearly Kaehler six-dimensional homogeneous space, and the manifolds RxG/H and R^2xG/H carry G_2- and Spin(7)-structures,…

In math.SG/0605587, we studied Yang-Mills functional on the space of connections on a principal G_R-bundle over a closed, connected, nonorientable surface, where G_R is any compact connected Lie group. In this sequel, we generalize the…

In this paper, we study the critical points of $F$-Yang-Mills functional on $\mathbb{C}P^n$, which are called $F$-Yang-Mills connections, which is a generalization of Yang-Mills connections. We prove that if…

Let M be a manifold with Grassmann structure, i.e. with an isomorphism of the cotangent bundle T^*M\cong E\otimes H with the tensor product of two vector bundles E and H. We define the notion of a half-flat connection \nabla^W in a vector…

In this work, we introduce a novel approach to the problem of gauge choice for the Yang-Mills equation on the Minkowski space $\mathbb{R}^{1+3}$, which uses the Yang-Mills heat flow in a crucial way. As this approach does not possess the…

Massless Dirac equation for spinor multiplets is minimally coupled with a unitary representation of an arbitrary compact semisimple gauge group. The spectrum of the second quantized interaction Hamiltonian has a positive mass gap running…

We give three short proofs of the Makeenko-Migdal equation for the Yang-Mills measure on the plane, two using the edge variables and one using the loop or lasso variables. Our proofs are significantly simpler than the earlier pioneering…

Phenomenological compactifications of M-theory involve 7-manifolds with G_2 holonomy and various singularities. Here we study local geometries with such singularities, by thinking of them as compactifications of 7d supersymmetric Yang-Mills…

In this paper we explain how Morse theory for the Yang-Mills functional can be used to prove an analogue, for surface groups, of the Atiyah-Segal theorem. Classically, the Atiyah-Segal theorem relates the representation ring R(\Gamma) of a…