Related papers: ABJM Matrix Model and 2D Toda Lattice Hierarchy
We develop a systematic procedure of finding integrable ''relativistic'' (regular one-parameter) deformations for integrable lattice systems. Our procedure is based on the integrable time discretizations and consists of three steps. First,…
Toda lattice and minimal surfaces are related to each other through Allen-Cahn equation. In view of the structure of the solutions of the Toda lattice, we find new balancing configuration using techniques of integrable systems. This allows…
There are two-dimensional Toda field equations corresponding to each (finite or affine) Lie algebra. The question addressed in this note is whether there exist integrable discrete versions of these. It is shown that for certain algebras…
In this paper, we construct a new integrable equation which is a generalization of $q$-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of the generalized $q$-Toda…
We give a construction of completely integrable $(2m)$-dimensional Hamiltonian systems with cubic Hamilton functions. The construction depends on a constant skew-Hamiltonian matrix $A$, that is, a matrix satisfying $A^{\rm T}J=JA$, where…
Four integrable symplectic maps approximating two Hamiltonian flows from the relativistic Toda hierarchy are introduced. They are demostrated to belong to the same hierarchy and to examplify the general scheme for symplectic maps on groups…
The aim of this paper is to summarize some recently obtained relations between the Ablowitz-Ladik hierarchy (ALH) and other integrable equations. It has been shown that solutions of finite subsystems of the ALH can be used to derive a wide…
The integrability of a family of hamiltonian systems, describing in a particular case the motionof N ``peakons" (special solutions of the so-called Camassa-Holm equation) is established in the framework of the $r$-matrix approach, starting…
It is shown how to study the 2-D Toda system for SU(n+1) using Nevanlinna theory of meromorphic functions and holomorphic curves. The results generalize recent results of Jost - Wang and Chen - Li.
We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach, we present the field equations of this model as a bilinear…
Based on the recent indications of integrability in the planar ABJ model, we conjecture an exact expression for the interpolating function h(\lambda_1,\lambda_2) in this theory. Our conjecture is based on the observation that the…
R-matrix is explicitly constructed for simplest representations of the Ding-Iohara-Miki algebra. The calculation is straightforward and significantly simpler than the one through the universal R-matrix used for a similar calculation in the…
Recently we showed how, in two-dimensional scalar theories, one-loop threshold diagrams can be cut into the product of one or more tree-level diagrams arXiv:2206.09368. Using this method on the ADE series of Toda models, we computed the…
An integrable self-adjoint 7-point scheme on the triangular lattice and an integrable self-adjoint scheme on the honeycomb lattice are studied using the sublattice approach. The star-triangle relation between these systems is introduced,…
A new representation of the 2N fold integrals appearing in various two-matrix models that admit reductions to integrals over their eigenvalues is given in terms of vacuum state expectation values of operator products formed from…
We generalize the Toda lattice hierarchy by considering N+M dependent variables. We construct roots and logarithms of the Lax operator which are uniquely defined operators with coefficients that are $\epsilon$-series of differential…
A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda equation, is shown to have a Lax formalism and an infinite hierarchy of higher flows. The Lax formalism is very similar to the case of the self-dual vacuum…
We investigate several aspects of BPS latitude Wilson loops in gauge theories in three dimensions with $\mathcal{N}\ge 4$ supersymmetry. We derive a matrix model for the bosonic latitude Wilson loop in ABJM using supersymmetric…
In this paper, we give an unstable approach of the May-Lawrence matrix Toda bracket, which becomes a useful tool for the theory of determinations of unstable homotopy groups. Then, we give a generalization of the classical isomorphisms…
In the ABJM model, we study the three-point function of two heavy operators and an (ir)relevant one. Following the AdS/CFT correspondence, the structure constant in the large 't Hooft coupling limit can be factorized into two parts. One is…