Related papers: Generalized Toda Field Theories
The classical hierarchy of Toda flows can be thought of as an action of the (abelian) group of polynomials on Jacobi matrices. We present a generalization of this to the larger groups of $C^2$ and entire functions, and in this second case,…
We consider a nonlinear field equation which can be derived from a binomial lattice as a continuous limit. This equation, containing a perturbative friction-like term and a free parameter $\gamma$, reproduces the Toda case (in absence of…
We study the quantum integrability of nonsimply--laced affine Toda theories defined on the half--plane and explicitly construct the first nontrivial higher--spin charges in specific examples. We find that, in contradistinction to the…
Toda Conformal Field Theories (CFTs hereafter) are generalizations of Liouville CFT where the underlying field is no longer scalar but takes values in a finite-dimensional vector space induced by a complex simple Lie algebra. The goal of…
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…
We analyze multi--matrix chain models. They can be considered as multi--component Toda lattice hierarchies subject to suitable coupling conditions. The extension of such models to include extra discrete states requires a weak form of…
For any classical Lie algebra $g$, we construct a family of integrable generalizations of Toda mechanics labeled a pair of ordered integers $(m,n)$. The universal form of the Lax pair, equations of motion, Hamiltonian as well as Poisson…
The massive phase of two-layer integrable systems is studied by means of RSOS restrictions of affine Toda theories. A general classification of all possible integrable perturbations of coupled minimal models is pursued by an analysis of the…
We derive an explicit, exactly conformally invariant form for the action for the non-abelian Toda field theory. We demonstrate that the conformal invariance conditions, expressed in terms of the $\beta$-functions of the theory, are…
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…
We express the Poisson brackets of local fields of the affine Toda field theories in terms of the Drinfeld-Sokolov dressing operator. For this, we introduce a larger space of fields, containing ``half screening charges'' and ``half…
Massive integrable field theories in $1+1$ dimensions are defined at the Lagrangian level, whose classical equations of motion are related to the ``non-abelian'' Toda field equations. They can be thought of as generalizations of the…
A folding process is applied to fused a^(1)_r defects to construct defects for the non-simply laced affine Toda field theories of c^(1)_n, d^(2)_n and a^(2)_2n at the classical level. Support for the hypothesis that these defects are…
Invariance under non-linear ${\sf {\hat W}}_{\infty}$ algebra is shown for the two-boson Liouville type of model and its algebraic generalizations, the extended conformal Toda models. The realization of the corresponding generators in terms…
The affine Toda field theory is studied as a 2+1-dimensional system. The third dimension appears as the discrete space dimension, corresponding to the simple roots in the $A_N$ affine root system, enumerated according to the cyclic order on…
In this note we show that the single soliton solutions known previously in the $1+1$ dimensional affine Toda field theories from a variety of different methods \cite{H1,MM,OTUa,OTUb}, are in fact not the most general single soliton…
The leading and the subleading Landau singularities in affine Toda field theories are examined in some detail. Formulae describing the subleading simple pole structure of box diagrams are given explicitly. This leads to a new and nontrivial…
We study the Toda field theory with finite Lie algebras using an extension of the Goulian-Li technique. In this way, we show that, after integrating over the zero mode in the correlation functions of the exponential fields, the resulting…
Affine Toda field theory with a pure imaginary coupling constant is a non-hermitian theory. Therefore the solutions of the equation of motion are complex. However, in $1+1$ dimensions it has many soliton solutions with remarkable…
We restrict affine Toda field theory to the half-line by imposing certain boundary conditions at $x=0$. The resulting theory possesses the same spectrum of solitons and breathers as affine Toda theory on the whole line. The classical…