Related papers: Toda-Heisenberg chain: interacting sigma-fields in…
We consider an 8--dimensional gravitational theory, which possesses a principle fiber bundle structure, with Lorentz--scalar fields coupled to the metric. One of them plays the role of a Higgs field and the other one that of a dilaton…
We establish the equivalence of a 2D contour dynamics to the dispersionless limit of the integrable Toda hierarchy constrained by a string equation. Remarkably, the same hierarchy underlies 2D quantum gravity.
We study the deep connection between integrable models and Poisson-Lie T-duality working on a finite dimensional example constructed on SL(2,C) and its Iwasawa factors SU(2) and B. We shown the way in which Adler-Kostant-Symes theory and…
Hyperbolic versions of the integrable (1+1)-dimensional Heisenberg Ferromagnet and sigma models are discussed in the context of topological solutions classifiable by an integer `winding number'. Some explicit solutions are presented and the…
A range of bosonic models can be expressed as (sometimes generalized) $\sigma$-models, with equations of motion coming from a selfduality constraint. We show that in D=2, this is easily extended to supersymmetric cases, in a superspace…
2D nonlinear sigma models with Hermitian symmetric target admit a theta-term, which couples the field theory to the topological charge of its instanton gas. At the special coupling theta = pi, by what is nowadays attributed to a…
The correlated fermionic many-particle system, near infinite scattering length, reveals an underlying Heisenberg symmetry in one dimension, as compared to an $SO(2,1)$ symmetry in two dimensions. This facilitates an exact map from the…
New classes of classically integrable models in the cosmological theories with a scalar field are obtained by using freedoms of defining time and fields. In particular, some models with the sum of exponential potentials in the flat spatial…
The conformal affine sl(2) Toda model coupled to matter field is treated as a constrained system in the context of Faddeev-Jackiw and the (constrained) symplectic schemes. We recover from this theory either, the sine-Gordon or the massive…
The Inozemtsev chain is an exactly solvable interpolation between the short-range Heisenberg and long-range Haldane-Shastry (HS) chains. In order to unlock its potential to study spin interactions with tunable interaction range using the…
We study the massive ODE/IM correspondence for modified $B_2^{(1)}$ affine Toda field equation. Based on the $\psi$-system for the solutions of the associated linear problem, we obtain the Bethe ansatz equations. We also discuss the T-Q…
The dispersionless Toda hierarchy turns out to lie in the heart of a recently proposed Landau-Ginzburg formulation of two-dimensional string theory at self-dual compactification radius. The dynamics of massless tachyons with discrete…
Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schr\"odinger family of…
Solutions in multidimensional gravity with m p-branes related to Toda-like systems (of general type) are obtained. These solutions are defined on a product of n+1 Ricci-flat spaces M_0 x M_1 x...x M_n and are governed by one harmonic…
We present a study of a quasi-integrable deformation of the three-particle open Toda chain, constructed by introducing a translation-invariant three-body interaction terms. Although this modification explicitly breaks the exact…
We show that the three strings vertex coefficients in light--cone open string field theory satisfy the Hirota equations for the dispersionless Toda lattice hierarchy. We show that Hirota equations allow us to calculate the correlators of an…
We consider a theory of scalar superfields in two dimensions with arbitrary superpotential. By imposing no particle production in tree level scattering, we constrain the form of the admissible interactions, recovering a supersymmetric…
In this paper we discuss the relation between the functions that give first integrals of full symmetric Toda system (an important Hamilton system on the space of traceless real symmetric matrices) and the vector fields on the group of…
We show that the equality of 2d $\mathcal{N}$=(2,2) supersymmetric indices in Seiberg-type duality leads to a new integrable Ising-type model. The emergence of the new model is the result of correspondence between the supersymmetric $SU(2)$…
The 2-dimensional space-time sine-Gordon field theory is extended algebraically within the n-dimensional space of extended complex numbers. This field theory is constructed in terms of an adapted extension of standard vertex operators. A…