相关论文: N=4 Multi-Particle Mechanics, WDVV Equation and Ro…

We present the complete integrands of five-point superamplitudes in N=4 super-Yang-Mills theory and N=8 supergravity, at one and two loops, for four-dimensional external states and D-dimensional internal kinematics. For N=4 super-Yang-Mills…

In this paper we study Open Wilson Lines (OWL's) in the context of two Supersymmetric Yang Mills theories. First we consider four dimensional N=2 Supersymmetric Yang Mills Theory with hypermultiplets transforming in the fundamental…

We investigate the geometry of the matrix model associated with an N=1 super Yang-Mills theory with three adjoint fields, which is a massive deformation of N=4. We study in particular the Riemann surface underlying solutions with arbitrary…

The N=4 SuperYang--Mills theory is covariantly determined by a U(1) \times SU(2) \subset SL(2,R) \times SU(2) internal symmetry and two scalar and one vector BRST topological symmetry operators. This determines an off-shell closed sector of…

We discuss integrable extensions of real nonlinear wave equations with multi-soliton solutions, to their bicomplex, quaternionic, coquaternionic and octonionic versions. In particular, we investigate these variants for the local and…

The simplest non-trivial solutions of WDVV equations are A_n and B_n-potentials, which describe metrics of K.Saito on spaces of versal deformation of A_n and B_n-singularities. These are some polynomials, which were known for $n\leqslant$…

The paper contains some new results and a review of recent achievements, concerning the multisupport solutions to matrix models. In the leading order of the 't Hooft expansion for matrix integral, these solutions are described by…

We study orbifolds of ${\cal N} = 4$ U(n) super-Yang-Mills theory given by discrete subgroups of SU(2) and SU(3). We have reached many interesting observations that have graph-theoretic interpretations. For the subgroups of SU(2), we have…

A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian (``acceleration equal force'') equations of motion, featuring one-body (``external'') and pair (``interparticle'') forces. The…

In this contribution we summarize our recent progress in understanding the relation between ${\cal N} = 1$ superconformal indices and relativistic elliptic integrable models. We start briefly reviewing the emergence of such models in…

We study a new class of inhomogeneous pp-wave solutions with 8 unbroken supersymmetries in D=11 supergravity. The 9 dimensional transverse space is Euclidean and split into 3 and 6 dimensional subspaces. The solutions have non-constant…

Differential equations for scaling relation of prepotential in N=2 supersymmetric SU(2) Yang-Mills theory coupled with massive matter hypermultiplet are proposed and are explicitly demonstrated in one flavour ($N_f =1$) theory. By applying…

We study the N=4 harmonic superparticle model, both with and without central charge and quantize it. Since the central charge breaks the U(4) R-symmetry group of the N=4 superalgebra down to USp(4), we consider the superparticle dynamics in…

The quantization procedure for both N=1 and N=2 supersymmetric Korteweg-de Vries (SUSY KdV) hierarchies is constructed. Namely, the quantum counterparts of the monodromy matrices, built by means of the integrated vertex operators, are shown…

An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…

There exist many four dimensional integrable theories. They include self-dual gauge and gravity theories, all their extended supersymmetric generalisations, as well the full (non-self-dual) N=3 super Yang-Mills equations. We review the…

We present the results of further analysis of the integrability properties of the $N=4$ supersymmetric KdV equation deduced earlier by two of us (F.D. \& E.I.) as a hamiltonian flow on $N=4$ $SU(2)$ superconformal algebra in the harmonic…

We describe various approaches that give matrix descriptions of compactified NS five-branes. As a result, we obtain matrix models for Yang-Mills theories with sixteen supersymmetries in dimensions $2,3,4$ and 5. The equivalence of the…

An elementary introduction to the 2d/4d correspondences is given. After quickly reviewing the 2d q-deformed Yang-Mills theory and the Liouville theory, we will introduce 4d theories obtained by coupling trifundamentals to SU(2) gauge…

N=2 supersymmetric U(N) Yang-Mills theory softly broken to N=1 by the superpotential of the adjoint scalar fields is discussed from the viewpoint of the Whitham deformation theory for prepotential. With proper identification of the…