Related papers: On the construction of solutions to the Yang-Mills…
We describe a glueing construction for a certain self-dual reduction of the Yang-Mills equations in dimension 8.
The self-duality Yang-Mills equations in pseudoeuclidean spaces of dimensions $d\leq 8$ are investigated. New classes of solutions of the equations are found. Extended solutions to the D=10, N=1 supergravity and super Yang-Mills equations…
In this paper, a procedure which gives euclidean solutions of 3-dimensional Einstein-Yang-Mills equations when one has solutions of the Einstein equations is proposed. The method is based on reformulating Yang-Mills theory in such a way…
By employing the higher dimensional version of the Wu-Yang Ansatz we obtain black hole solutions in the spherically symmetric Einstein-Yang-Mills (EYM) theory. Although these solutions were found recently by other means, our method provides…
The new approach to quantum mechanical problems is proposed. Quantum states are represented in an algebraic program, by lists of variable length, while operators are well defined functions on these lists. Complete numerical solution of a…
For gauge groups SO$(n{+}1)$, SU$(m{+}1)$ and Sp$(\ell{+}1)$, we construct equivariant Yang-Mills solutions on de Sitter space in $n{+}1$, $2(m{+}1)$ and $4(\ell{+}1)$ spacetime dimensions. The latter is conformally mapped to a finite…
The solution of symmetry equation of Yang-Mills self dual system is found in explicit form of its raising Hamiltonian operator. Thus explicit form of equations of self dual Yang Mills hierarchy is constructed.
Yang-Mills theory is studied in three dimensions using the equations of motion of the $1$PI and $3$PI effective actions. The employed self-contained truncation includes the propagators, the three-point functions and the four-gluon vertex…
A residue formula which evaluates any correlation function of topological $SU_n$ Yang-Mills theory with arbitrary magnetic flux insertion in two dimensions are obtained. Deformations of the system by two form operators are investigated in…
We study regular, static, spherically symmetric solutions of Yang-Mills theories employing higher order invariants of the field strength coupled to gravity in $d$ dimensions. We consider models with only two such invariants characterised by…
Higher-point functions in N = 4 super Yang-Mills theory can be constructed using integrability by triangulating the surfaces on which Feynman graphs would be drawn. It remains hard to analytically compute the necessary re-gluing of the…
We solve exactly the Dyson-Schwinger equations for Yang-Mills theory in 3 and 4 dimensions. This permits us to obtain the exact correlation functions till order 2. In this way, the spectrum of the theory is straightforwardly obtained and…
We consider the ambitwistor description of $\mathcal N$=4 supersymmetric extension of U($N$) Yang-Mills theory on Minkowski space $\mathbb R^{3,1}$. It is shown that solutions of super-Yang-Mills equations are encoded in real analytic…
The rigorous construction of quantum Yang-Mills theories, especially in dimension four, is one of the central open problems of mathematical physics. Construction of Euclidean Yang-Mills theories is the first step towards this goal. This…
The equations of a relative equilibrium in a pure Yang--Mills gauge theory with the Coulomb gauge fixing are obtained. They are derived as a direct consequence of the results of our previous work on Wong's equations in gauge theory.The…
We advocate a method to improve systematically the self-consistent harmonic approximation (or the Gaussian approximation), which has been employed extensively in condensed matter physics and statistical mechanics. We demonstrate the {\em…
We show how to formulate Yang-Mills Theory in \m{2+1} dimensions as a hamitonian system within a simplicial regularization and construct its quantization, with special attention to the mass gap. An approximate conformal invariance of the…
We derive an explicit formula for the vertex amplitude of dual SU(2) Yang-Mills theory in four dimensions on the lattice, and provide an efficient algorithm (of order j to the fourth power) for its computation. This opens the way for both…
Yang-Mills theories are an important building block of the standard model and in particular of quantum chromodynamics. Its correlation functions describe the behavior of its elementary particles, the gauge bosons. In quantum chromodynamics,…
This is a survey of recent studies of singularity formation in solutions of spherically symmetric Yang-Mills equations in higher dimensions. The main attention is focused on five space dimensions because this case exhibits interesting…