Related papers: Morse index stability for Yang-Mills connections
In this paper we prove that there is a neighborhood in the $C^2$ topology of the usual metric on the Euclidean sphere $S^n (n\geq 5)$ such that there is no nontrivial weakly stable Yang-Mills connections for any metric $\tilde{g}$ in this…
The stability of Yang-Mills bundles over the usual $S^4$ space-time manifold is investigated according to the topological methods. The necessary gauge- and topological invaraint criterion for the exsitence of the related critical points is…
We calculate the exact values of the holomorphic observables of {\cal N}=4 supersymmetric SU(N) Yang-Mills theory deformed by mass terms which preserve {\cal N}=1 SUSY. These include the chiral condensates in each massive vacuum of the…
We investigate hermitian Yang-Mills connections on pullback bundles with respect to adiabatic classes on the total space of holomorphic submersions with connected fibres. Under some technical assumptions on the graded object of a…
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…
Here we provide refinements of the stability results of Simons and Xin, concerning the stability of Yang-Mills fields and harmonic maps respectively. The result also implies the earlier Morse index estimates for both cases.
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 give an algebraic criterion for the existence of projectively Hermitian-Yang-Mills metrics on a holomorphic vector bundle $E$ over some complete non-compact K\"ahler manifolds $(X,\omega)$, where $X$ is the complement of a divisor in a…
We study ${\mathcal N} = 1$ $SU(N)$ super Yang-Mills (SYM) theory on $\mathbb{R}^2\times (S^1)_3\times (S^1)_4$ with the 't Hooft twist. The theory becomes weakly coupled if the length $L_4$ of $(S^1)_4$ is sufficiently small,…
There exists a small family of analytic SO(4)-invariant but time-dependent SU(2) Yang-Mills solutions in any conformally flat four-dimensional spacetime. These might play a role in early-universe cosmology for stabilizing the symmetric…
Given a principal bundle $P\to M$ over a Riemannian manifold with compact structure group $G$, let us consider a stationary Yang-Mills connection $A$ with energy $\int_M |F_A|^2\le \Lambda$. If we consider a sequence of such connections…
The space of Sobolev connections, as it has been introduced for studying the variation of Yang-Mills Lagrangian in the critical dimension $4$, happens not to be weakly sequentially complete in dimension larger than $4$. This is a major…
We study the weak continuity of two interrelated non-linear partial differential equations, the Yang-Mills equations and the Gau{\ss}-Codazzi-Ricci equations, involving $L^p$-integrable connections. Our key finding is that underlying…
The gravitational instability of Yang-Mills cosmologies is numerically studied with the hamiltonian formulation of the spherically symmetric Einstein-Yang-Mills equations with SU(2) gauge group. On the short term, the expansion dilutes the…
In this paper we study the behaviour of critical points of the Ginzburg-Landau perturbation of the Dirichlet energy into the sphere $E_\varepsilon(u):=\int_\Sigma \frac{1}{2}|du|^2_h\ \,dvol_h…
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…
Following work of Colding-Minicozzi, we define a notion of entropy for connections over $\mathbb R^n$ which has shrinking Yang-Mills solitons as critical points. As in Colding-Minicozzi, this entropy is defined implicitly, making it…
We prove that in the limit of the coupling going to infinity a Yang-Mills theory is equivalent to a $\lambda\phi^4$ theory with the dynamics ruled just by a homogeneous equation. This gives explicitly the Green function and the mass…
We present some of the latest results from our numerical investigations of N=4 supersymmetric Yang--Mills theory formulated on a space-time lattice. Based on a construction that exactly preserves a single supersymmetry at non-zero lattice…
SU(2) Yang-Mills Theory coupled to massive adjoint scalar matter is studied in (1+1) dimensions using Discretised Light-Cone Quantisation. This theory can be obtained from pure Yang-Mills in 2+1 dimensions via dimensional reduction. On the…