Related papers: Affine Toda field theory as a 3-dimensional integr…
The exact eigenvalues of the infinite set of conserved charges on the multi-particle states in affine Toda theories are determined. This is done by constructing a free field realization of the Zamolodchikov-Faddeev algebra in which the…
We study the affine quasi-Einstein equation, a second order linear homogeneous equation, which is invariantly defined on any affine manifold. We prove that the space of solutions is finite-dimensional, and its dimension is a strongly…
The aim of this work is focused on the investigation of the algebraic complete integrability of the Toda lattice associated with the twisted affine Lie algebra $a_4^{(2)}$. First, we prove that the generic fiber of the momentum map for this…
A large class of real $3$-dimensional nilpotent polynomial vector fields of arbitrary degree is considered. The aim of this work is to present general properties of the discrete and continuous dynamical systems induced by these vector…
In the article a classification method for nonlinear integrable equations with three independent variables is discussed based on the notion of the integrable reductions. We call the equation integrable if it admits a large class of…
We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approaches with an emphasis on the second approach. The first…
The Eguchi-Hanson, Taub-NUT and Atiyah-Hitchin metrics are the only complete non-singular SO(3)-invariant hyper-Kahler metrics in four dimensions. The presence of a rotational SO(2) isometry allows for their unified treatment based on…
Recent work of Foda and his group on a connection between classical integrable hierarchies (the KP and 2D Toda hierarchies) and some quantum integrable systems (the 6-vertex model with DWBC, the finite XXZ chain of spin 1/2, the phase model…
Soliton time-delays and the semiclassical limit for soliton S-matrices are calculated for non-simply laced Affine Toda Field Theories. The phase shift is written as a sum over bilinears on the soliton conserved charges. The results apply to…
We study the possible dynamical degrees of automorphisms of the affine space $\mathbb{A}^n$. In dimension $n=3$, we determine all dynamical degrees arising from the composition of an affine automorphism with a triangular one. This…
The multicomponent 2D Toda hierarchy is analyzed through a factorization problem associated to an infinite-dimensional group. A new set of discrete flows is considered and the corresponding Lax and Zakharov--Shabat equations are…
Differential-difference integrable exponential type systems are studied corresponding to the Cartan matrices of semi-simple or affine Lie algebras. For the systems corresponding to the algebras $A_2$, $B_2$, $C_2$, $G_2$ the complete sets…
We present a variational theory of integrable differential-difference equations (semi-discrete integrable systems). This is a natural extension of the ideas known by the names "Lagrangian multiforms" and "Pluri-Lagrangian systems", which…
We discuss a particular stringy modular cosmology with two axion fields in seven space-time dimensions, decomposable as a time and two flat three-spaces. The effective equations of motion for the problem are those of the $SU(3)$ Toda…
Many integrable theories can be formulated universally in terms of Lie algebraic root systems. Well-studied are conformally invariant scalar field theories of Toda type and their massive versions, which can be expressed in terms of simple…
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 find a sequence consisting of time dependent evolution vector fields whose time independent part corresponds to the master symmetries for the Toda equations. Each master symmetry decomposes as a sum consisting of a group symmetry and a…
The non-conformal analog of abelian T-duality transformations relating pairs of axial and vector integrable models from the non abelian affine Toda family is constructed and studied in detail.
We broaden the scope of quantum field theory by introducing a general class of discrete gauge theories that realize either topological order or fracton behavior across dimensions. We start from translation-invariant systems endowed with…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…