Related papers: Some new integrable equations from the self-dual Y…
By using the self-dual Yang-Mills (SDYM) equation as an example, we study a method for relating symmetries and recursion operators of two partial differential equations connected to each other by a non-auto-Backlund transformation. We prove…
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…
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…
We construct static solutions to a SU(2) Yang--Mills (YM) dilaton model in 4+1 dimensions subject to bi-azimuthal symmetry. The YM sector of the model consists of the usual YM term and the next higher order term of the YM hierarchy, which…
In the present work we analyse $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills (SYM) theory in two dimensions by means of lattice simulations. The theory arises as dimensional reduction of $\mathcal{N}=1$ SYM theory in four dimensions. As in…
The Einstein-Yang-Mills equations are the source of many interesting solutions within general relativity, including families of particle-like and black hole solutions, and critical phenomena of more than one type. These solutions,…
Certain features associated with the symmetry reduction of the vacuum Einstein equations by two commuting, space-like Killing vector fields are studied. In particular, the discussion encompasses the equations for the Gowdy $T^3$ cosmology…
We propose an extension of the Yang-Mills paradigm from Lie algebras to internal chiral superalgebras. We replace the Lie algebra-valued connection one-form $A$, by a superalgebra-valued polyform $\widetilde{A}$ mixing exterior-forms of all…
Principal chiral models on a d-1 dimensional simplex are introduced and studied analytically in the large $N$ limit. The $d = 0, 2, 4$ and $\infty$ models are explicitly solved. Relationship with standard lattice models and with few-matrix…
In this paper we present novel integrable symplectic maps, associated with ordinary difference equations, and show how they determine, in a remarkably diverse manner, the integrability, including Lax pairs and the explicit solutions, for…
The anti-self-dual Yang-Mills equations are known to have reductions to many integrable differential equations. A general B\"acklund transformation (BT) for the ASDYM equations generated by a Darboux matrix with an affine dependence on the…
We present arguments for the existence of a new type of solutions of the Euclidean Einstein-Yang-Mills-dilaton theory in $d=4$ dimensions. Possesing nonvanishing nonabelian charges, these nonselfdual configurations have no counterparts on…
We demonstrate that the general (A)dS-Kerr-NUT solutions in D dimensions with ([D/2], [(D+1)/2]) signature admit [D/2] linearly-independent, mutually-orthogonal and affinely-parameterised null geodesic congruences. This enables us to write…
We show that $~N=1$~ {\it supersymmetric} Kadomtsev-Petviashvili (SKP) equations can be embedded into recently formulated $~N=1$~ self-dual {\it supersymmetric} Yang-Mills theories after appropriate dimensional reduction and truncation,…
We establish a new non-minimal Einstein-Yang-Mills-dilaton model, for which the Lagrangian is linear in the curvature and contains eight arbitrary functions of the scalar (dilaton) field. The self-consistent system of equations for the…
A multi-parameter integrable deformation of the principal chiral model is presented. The Yang-Baxter and bi-Yang-Baxter sigma-models, the principal chiral model plus a Wess-Zumino term and the TsT transformation of the principal chiral…
It is shown that there exists an on-shell light cone gauge where half of the fermionic components of the super vector potential vanish, so that part of the superspace flatness conditions becomes linear. After reduction to $(1+1)$ space-time…
The reduction by restricting the spectral parameters $k$ and $k'$ on a generic algebraic curve of degree $\mathcal{N}$ is performed for the discrete AKP, BKP and CKP equations, respectively. A variety of two-dimensional discrete integrable…
We study the class of six-dimensional $\Lambda$-vacuum spacetimes which admit a non-degenerate multiple Weyl aligned null direction l (thus being of Weyl type~II or more special) with a ``generic'' optical matrix. Subject to an additional…
The Schwinger-Dyson equations in the ladder approximation for $2D$ induced gravity coupled to fermions on a flat background are obtained in conformal gauge. A numerical study of these equations shows the possiblity of chiral symmetry…