Related papers: An energy gap for Yang-Mills connections

We consider the CR Yamabe equation with critical Sobolev exponent on a closed contact manifold M of dimension 2n + 1. The problem of finding solutions with minimum energy has been resolved for all dimensions except dimension 5 (n = 2). In…

We consider a $3$-manifold $M$ equipped with nondegenerate contact form $\lambda$ and compatible almost complex structure $J$. We show that if the data $(M, \lambda, J)$ admits a stable finite energy foliation, then for a generic choice of…

We show that the quantization of energy for Willmore spheres into closed Riemannian manifolds holds provided that the Willmore energy and the area are uniformly bounded. The analogous energy quantization result holds for Willmore surfaces…

For the quantized Yang-Mills $3+1$ dimensional problem we introduce the Wilson loop, prove an extension of Elitzur's theorem and shown quark confinement for sufficiently small values of the bare coupling constant, provided the existence of…

In this monograph, we develop results on global existence and convergence of solutions to abstract gradient flows on Banach spaces for a potential function that obeys the Lojasiewicz-Simon gradient inequality. We prove a Lojasiewicz-Simon…

Given a principal bundle on an orientable closed surface with compact connected structure group, we endow the space of based gauge equivalence classes of smooth connections relative to smooth based gauge transformations with the structure…

We establish the lower semi continuity of the Morse index and the upper continuity of the Morse Index plus nullity of sequences of critical points of the Sacks-Uhlenbeck type relaxation of the Yang-Mills Energy in 4 dimension. The result is…

We show that if a closed $C^1$-smooth surface in a Riemannian manifold has bounded Kolasinski--Menger energy, then it can be triangulated with triangles whose number is bounded by the energy and the area. Each of the triangles is an image…

This article is devoted to the energy critical hyperbolic Yang--Mills system in the $(4+1)$ dimensional Minkowski space, which is considered by the authors in a sequence of four papers. The final outcome of these papers is twofold: (i) the…

We consider the Hermitian Yang-Mills (instanton) equations for connections on vector bundles over a 2n-dimensional K\"ahler manifold X which is a product Y x Z of p- and q-dimensional Riemannian manifold Y and Z with p+q=2n. We show that in…

We construct a spectral triple on a quantum Heisenberg manifold, which generalizes the results of Chakraborty and Shinha, and associate to it an energy functional on the set of projections, following the approach of Mathai-Rosenberg to…

The moduli space of flat connections for maximally supersymmetric Yang-Mills theories, in a space-time of the form T^3xR, contains isolated points, corresponding to normalizable zero energy states, for certain simple gauge groups G. We…

In this note we summarize some of the results found recently in hep-th/0609054. We show the pure discretness of the non-perturbative quantum spectrum of a symplectic Yang-Mills theory defined on a Riemann surface of positive genus, living…

Pure lattice SU(2) Yang-Mills theory in five dimensions is considered, where an extra dimension is compactified on a circle. Monte-Carlo simulations indicate that the theory possesses a continuum limit with a non-vanishing string tension if…

It is shown that the quantum ground state energy of particle of mass m and electric charge e moving on a compact Riemann surface under the influence of a constant magnetic field of strength B is E_0=eB/2m. Remarkably, this formula is…

Lie algebroid Yang-Mills theories are a generalization of Yang-Mills gauge theories, replacing the structural Lie algebra by a Lie algebroid E. In this note we relax the conditions on the fiber metric of E for gauge invariance of the action…

We investigate the asymptotic behavior of the $\mathrm{SU}(2)$-Yang-Mills-Higgs energy $E(\Phi,A)=\int_M|d_A\Phi|^2+|F_A|^2$ in the large mass limit, proving convergence to the codimension-three area functional in the sense of De Giorgi's…

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…

If X is a full, finitely generated, projective module over a non-commutative torus, the Yang-Mills functional attains its minimum exactly on the flat connections on X. We classify the flat connections on modules admitting integrable…

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…