Related papers: Exterior Differential Systems for Yang-Mills Theor…

The relation between two--dimensional integrable systems and four--dimen\-sional self--dual Yang--Mills equations is considered. Within the twistor description and the zero--curvature representation a method is given to associate self--dual…

Consideration of some perturbatively calculated gauge-invariant expectation values of local noncomposite operators in pure Yang-Mills theory indicates that those expectation values which are not dimension specific, and which are well…

Local solutions of the static, spherically symmetric Einstein-Yang-Mills (EYM) equations with SU(2) gauge group are studied on the basis of dynamical systems methods. This approach enables us to classify EYM solutions in the origin…

Utilizing a number of results of Dittmann, we investigate the nature of the Yang-Mills field over the eight-dimensional convex set, endowed with the Bures metric, of three-level quantum systems. Adopting a numerical strategy, we first…

We study the classical dynamics of mechanical model obtained from the light-cone version of SU(2) Yang-Mills field theory under the supposition of gauge potential dependence only on ``time'' along the light-cone direction. The computer…

Recently we have proposed a set of variables for describing the infrared limit of four dimensional SU(2) Yang-Mills theory. here we extend these variables to the general case of four dimensional SU(N) Yang-Mills theory. We find that the…

We give the overview of solution techniques for the general conformally-invariant linear and nonlinear wave equations centered around the idea of dimensional reductions by their symmetry groups. The efficiency of these techniques is…

We present a non-perturbative study of the phase diagram of 5d SU(2) Yang-Mills theory with one compact extra dimension on the lattice. Assuming at least a modest scale separation between the cutoff and the compactification scales leads to…

Using (partial) curvature flows and the transitive action of subgroups of O(d,Z) on the indices {1,...,d} of the components of the Yang-Mills curvature in an orthonormal basis, we obtain a nested system of equations in successively higher…

Faddeev and Niemi have proposed a reformulation of SU(2) Yang-Mills theory in terms of a U(1) gauge theory with 8 off-shell degrees of freedom. We present a solution to Faddeev and Niemi's formulation which does not solve the SU(2)…

The reduced properties and applications of Yangian Y(sl(2)) and Y(su(3)) algebras are discussed. By taking a special constraint, the representation of Y(su(3)) can be divided into three 3 * 3 blocks diagonal based on Gell-mann matrices. The…

We extend the theory of exterior differential systems from manifolds and their tangent bundles to Lie algebroids. In particular, we define the concept of an integral manifold of such an exterior differential system. We support our…

Some aspects of the relation between differential geometry of curves and surfaces and multidimensional soliton equations is discussed. The connection between multidimensional soliton equations and Self-dual Yang-Mills equation is studied.

We apply the theory of functors of Artin rings to prove the existence of a universal formal solution to a exterior differential system. We compute the tangent space and the obstruction theory of the funtor of Artin ring governing the…

We investigate to derive off-shell invariant twisted super Yang-Mills for N=2 in 2-dimensions and N=4 in 4-dimensions with a central charge by super connection ansatz formalism. We find off-shell invariant N=2 algebra with and without an…

Division algebras are used to explain the existence and symmetries of various sets of auxiliary fields for super Yang-Mills in dimensions $d=3,4,6,10$. (Contribution to G\"ursey Memorial Conference I: Strings and Symmetries)

SU(N) Yang-Mills integrals form a new class of matrix models which, in their maximally supersymmetric version, are relevant to recent non-perturbative definitions of 10-dimensional IIB superstring theory and 11-dimensional M-theory. We…

We give a new realization of $Y(sl_3)$ via Cartan-Weyl elements. An algebraic description of Yangian Double $DY(sl_3)$, explicit comultiplication formulas and universal R-matrix are obtained in these terms.

In 1+1 dimensions two different formulations exist of SU(N) Yang Mills theories in light-cone gauge; only one of them gives results which comply with the ones obtained in Feynman gauge. Moreover the theory, when considered in 1+(D-1)…

This is an elementary introduction to exterior differential systems motivated by two examples: minimal submanifolds and the isometric embedding problem. The two main goals of the lectures are: 1. To explain how to find an appropriate…