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

For closed and connected subgroups G of SO(n), we study the energy functional on the space of G-structures of a (compact) Riemannian manifold M, where G-structures are considered as sections of the quotient bundle O(M)/G. Then, we deduce…

In \cite{Zh} \cite{LY} Zhang, Luo and Yin initiated the study of Lagrangian submanifolds satisfying ${\rm \nabla^*} T=0$ or ${\rm \nabla^*\nabla^*}T=0$ in $\mathbb{C}^n$ or $\mathbb{CP}^n$, where $T ={\rm \nabla^*}\tilde{h}$ and $\tilde{h}$…

We develop a new perspective on principal bundles with connection as morphisms from the tangent bundle of the underlying manifold to a classifying dg-Lie groupoid. This groupoid can be identified with a lift of the inner homomorphisms…

The variational approach to the Hamilton formulation of Yang-Mills theory in Coulomb gauge developed by the present authors previously is applied to Yang-Mills theory in 2+1 dimensions and is confronted with the existing lattice data. We…

A strong coupling expansion of the SU(2) Yang-Mills quantum Hamiltonian is carried out in the form of an expansion in the number of spatial derivatives, using the symmetric gauge \epsilon_{ijk} A_{jk}=0. Introducing an infinite lattice with…

We have found analytical self-dual solutions within the generalized Yang-Mills-Higgs model introduced in Phys. Rev. D 86, 085034 (2012). Such solutions are magnetic monopoles satisfying Bogomol'nyi-Prasad-Sommerfield (BPS) equations and…

The 3+1 dimensional Yang-Mills theory with the Pontryagin term included is studied on manifolds with a boundary. Based on the geometry of the universal bundle for Yang-Mills theory, the symplectic structure of this model is exhibited. The…

We show that the genus 34 Seiberg-Witten curve underlying $N=2$ Yang-Mills theory with gauge group $E_6$ yields physically equivalent results to the manifold obtained by fibration of the $E_6$ ALE singularity. This reconciles a puzzle…

We consider a class of lattice topological field theories, among which are the weak-coupling limit of 2d Yang-Mills theory and 3d Riemannian quantum gravity, whose dynamical variables are flat discrete connections with compact structure…

Self-dual Yang-Mills theory admits an underlying infinite dimensional symmetry algebra, which has been obtained from mode expansion of Mellin transformed 4d scattering amplitudes and separately, Koszul duality on twistor space. In this…

Given a hermitian line bundle $L\to M$ on a closed Riemannian manifold $(M^n,g)$, the self-dual Yang-Mills-Higgs energies are a natural family of functionals \begin{align*} &E_\epsilon(u,\nabla):=\int_M\Big(|\nabla…

We prove that a compact $RCD^*(0,N)$ (or equivalently $RCD(0,N)$) metric measure space, $\left(X, d, m \right)$, with $\diam X \le d$ and its first (nonzero) eigenvalue of the Laplacian (in the sense of Ambrosio-Gigli-Savar\'{e}) ,…

This work is a continuation of our previous work (JMP, Vol. 48, 12, pp. 122103-1-122103-20, 2007), where we constructed the non-relativistic Lee model in three dimensional Riemannian manifolds. Here we renormalize the two dimensional…

In this work we use constructs from the dual space of the semi-direct product of the Virasoro algebra and the affine Lie algebra of a circle to write a theory of gravitation which is a natural analogue of Yang-Mills theory. The theory…

This is an introductory chapter in a series in which we take a systematic study of the Yang-Mills equations on curved space-times. In this first, we provide standard material that consists in writing the proof of the global existence of…

The Yang-Mills (YM) equation in three spacetime dimensions (3D) can be modified to include a novel parity-preserving interaction term, with inverse mass parameter, in addition to a possible topological mass term. The novelty is that the…

In the context of D-dimensional Euclidean gravity, we define the natural generalisation to D-dimensions of the self-dual Yang-Mills equations, as duality conditions on the curvature 2-form of a Riemannian manifold. Solutions to these…

Long time existence and uniqueness of solutions to the Yang-Mills heat equation is proven over a compact 3-manifold with smooth boundary. The initial data is taken to be a Lie algebra valued connection form in the Sobolev space $H_1$. Three…

We construct and analyze a novel family of exact higher-dimensional black hole solutions in Einstein-Power-Yang-Mills gravity minimally coupled to a scalar field multiplet supporting a global monopole and a surrounding anisotropic ''scalar…

We show that classical, non-supersymmetric Yang-Mills theories coupled to spin-1/2 and spin-0 elementary matter fields, in (3+1)-dimensional Minkowski space-time, possess exact structures that resemble integrability, with an infinite number…