Related papers: On the geometry of classically integrable two-dime…
We discuss the integrability of 2d non-linear sigma models with target space being the squashed three-sphere, warped anti-de Sitter space and the Schroedinger spacetime. These models can be obtained via T-duality from integrable models. We…
A derivation of the Lax pair for the (1+1)-dimensional non-linear sigma-model is described. Its main benefit is to have a clearer physical origin and to allow the study of a generalization to higher dimensions.
In this article we review the Duistermaat-Heckman integration formula and the ensuing equivariant cohomology structure, in the finite dimensional case. In particular, we discuss the connection between equivariant cohomology and classical…
Non linear sigma models on Riemannian symmetric spaces constitute the most general class of classical non-linear sigma models which are known to be integrable. Using the current algebra structure of these models their canonical structure is…
We present a method to deform (generically non-abelian) T duals of two-dimensional $\sigma$ models, which preserves classical integrability. The deformed models are identified by a linear operator $\omega$ on the dualised subalgebra, which…
The equations that define the Lax pairs for generalized principal chiral models can be solved for any constant nondegenerate bilinear form on SU(2). Necessary conditions for the nonconstant metric on SU(2) that define the integrable models…
We show that SU(2)_L Yangian and q-deformed SU(2)_R symmetries are realized in a two-dimensional sigma model defined on a three-dimensional squashed sphere. These symmetries enable us to develop the two descriptions to describe its…
We show how to obtain the O(N) non-linear sigma model in two dimensions as a strong coupling limit of the corresponding linear sigma model. In taking the strong coupling limit, the squared mass parameter must be given a specific coupling…
We consider the sigma models where the base metric is proportional to the metric of the configuration space. We show that the corresponding sigma model equation admits a Lax pair. We also show that this type of sigma models in two…
We establish the isomorphism between a nonlinear $\sigma$-model and the abelian gauge theory on an arbitrary curved background, which allows us to derive integrable models and the corresponding Lax representations from gauge theoretical…
We establish the isomorphism between a nonlinear $\sigma$-model and the abelian gauge theory on an arbitrary curved background, which allows us to derive integrable models and the corresponding Lax representations from gauge theoretical…
The classical integrability the O(N) nonlinear sigma model on a half-line is examined, and the existence of an infinity of conserved charges in involution is established for the free boundary condition. For the case N=3 other possible…
A number of characteristics of integrable nonlinear partial differential equations (PDE's) for classical fields are reviewed, such as Backlund transformations, Lax pairs, and infinite sequences of conservation laws. An algebraic approach to…
Two-dimensional $\sigma$-models with $\mathbb{Z}_N$-symmetric homogeneous target spaces have been shown to be classically integrable when introducing WZ-terms in a particular way. This article continues the search for new models of this…
A review is given of some 2-dimensional metrics for which noncommutative versions have been found. They serve partially to illustrate a noncommutative extension of the moving-frame formalism. All of these models suggest that there is an…
For two-dimensional lattice equations one definition of integrability is that the model can be naturally and consistently extended to three dimensions, i.e., that it is "consistent around a cube" (CAC). As a consequence of CAC one can…
We investigate a relationship between a particular class of two-dimensional integrable non-linear $\sigma$-models and variations of Hodge structures. Concretely, our aim is to study the classical dynamics of the $\lambda$-deformed $G/G$…
A construction of conservation laws for chiral models (generalized sigma-models on a two-dimensional space-time continuum using differential forms is extended in such a way that it also comprises corresponding discrete versions. This is…
We construct a two dimensional nonlinear $\sigma$-model that describes the Hamiltonian flow in the loop space of a classical dynamical system. This model is obtained by equivariantizing the standard N=1 supersymmetric nonlinear…
It is pointed out that affine Lie algebras appear to be the natural mathematical structure underlying the notion of integrability for two-dimensional systems. Their role in the construction and classification of 2D integrable systems is…