相关论文: Energy gap for Yang-Mills connections, II: Arbitra…

A mathematically rigorous relativistic quantum Yang-Mills theory with an arbitrary semisimple compact gauge Lie group is set up in the Hamiltonian canonical formalism. The theory is non-perturbative, without cut-offs, and agrees with the…

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 extend the well-known Sacks-Uhlenbeck energy gap result (1981) for harmonic maps from closed Riemann surfaces into closed Riemannian manifolds from the case of maps with small energy (thus near a constant map), to the case of harmonic…

We prove global well-posedness of the $ 3d $ Yang-Mills equation in the temporal gauge in $ H^{\sigma} $ for $ \sigma > \frac{5}{6} $. Unlike related equations, Yang-Mills is not directly amenable to the method of almost conservation laws…

Fixing a constant $\lambda>0$, for any parameter $\varepsilon>0$ we study critical points of the Yang--Mills--Higgs energy \[ \mathcal{Y}_{\varepsilon}(\nabla,\Phi) = \int_M \varepsilon^2|F_{\nabla}|^2 + |\nabla\Phi|^2 +…

We define a conformally invariant action S on gauge connections on a closed pseudo-Riemannian manifold M of dimension 6. At leading order this is quadratic in the gauge connection. The Euler-Lagrange equations of S, with respect to…

On a two-dimensional Riemannian manifold without boundary we consider the variational limit of a family of functionals given by the sum of two terms: a Ginzburg-Landau and a perimeter term. Our scaling allows low-energy states to be…

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…

In this paper we prove gap theorems in Yang-Mills theory for complete four-dimensional manifolds with positive Yamabe constant. We extend the results of Gursky-Kelleher-Streets to complete manifolds. We also describe the equality in the gap…

A distance function on the set of physical equivalence classes of Yang-Mills configurations considered by Feynman and by Atiyah, Hitchin and Singer is studied for both the $2+1$ and $3+1$-dimensional Hamiltonians. This set equipped with…

We consider the minimum Yang-Mills energy on the complete $G_{2}$-manifolds and Calabi-Yau 3-folds,the connection $A$ is a stability Yang-Mills connection on the $G$-bundle $E$.We prove that the connection must be a $G_{2}$-instanton on…

We study pure Yang--Mills theory on $\Sigma\times S^2$, where $\Sigma$ is a compact Riemann surface, and invariance is assumed under rotations of $S^2$. It is well known that the self-duality equations in this set-up reduce to vortex…

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 >…

Let $\Sigma$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $\xi \colon P \to \Sigma$ be a principal $G$-bundle, and pick a…

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 find an argument related to the existence of a Z_2-symmetry for the renormalization group flow derived from the bare Yang-Mills Lagrangian, and show that the cancellation of the vacuum energy may arise motivated both from the…

We calculate the resummed perturbative free energy of ${\cal N} = 4$ supersymmetric Yang-Mills in four spacetime dimensions (SYM$_{44}$) to order $\lambda^{5/2}$ in the 't Hooft coupling at finite temperature and zero chemical potential.…

Let $\Sigma$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $\xi \colon P \to \Sigma$ be a principal $G$-bundle, and pick a…

On a smooth compact connected $d$-dimensional Riemannian manifold $M$, if $0 < s < d$ then an asymptotically equidistributed sequence of finite subsets of $M$ that is also well-separated yields a sequence of Riesz $s$-energies that…

We investigate Yang--Mills instanton theory over four dimensional asymptotically locally flat (ALF) geometries, including gravitational instantons of this type, by exploiting the existence of a natural smooth compactification of these…