Related papers: Hybrid classical integrability in squashed sigma m…
We give a short summary of our recent works on the classical integrable structure of two-dimensional non-linear sigma models defined on squashed three-dimensional spheres. There are two descriptions to describe the classical dynamics, 1)…
We proceed to study the hybrid integrable structure in two-dimensional non-linear sigma models with target space three-dimensional squashed spheres. A quantum affine algebra and a pair of Yangian algebras are realized in the sigma models…
We discuss classical integrable structure of two-dimensional sigma models which have three-dimensional Schrodinger spacetimes as target spaces. The Schrodinger spacetimes are regarded as null-like deformations of AdS_3. The original AdS_3…
We discuss a hidden symmetry of a two-dimensional sigma model on a squashed S^3. The SU(2) current can be improved so that it can be regarded as a flat connection. Then we can obtain an infinite number of conserved non-local charges and…
A master equation expressing the classical integrability of two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. In particular, a closer connection between integrability and T-duality…
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…
We proceed to study the integrable structures of two-dimensional non-linear sigma models defined on three-dimensional Schrodinger spacetimes. We show that anisotropic Lax pairs are equivalent with isotropic Lax pairs with flat conserved…
We consider the classical integrable structure of two-dimensional non-linear sigma models with target space three-dimensional Schrodinger spacetimes. There are the two descriptions to describe the classical dynamics: 1) the left description…
This paper deals with various interrelations between strings and surfaces in three dimensional ambient space, two dimensional integrable models and two dimensional and four dimensional decomposed SU(2) Yang-Mills theories. Initially, a…
A class of integrable 2-dim classical systems with integrals of motion of fourth order in momenta is obtained from the quantum analogues with the help of deformed SUSY algebra. With similar technique a new class of potentials connected with…
Supersymmetry breaking by the quantum deformation of a classical moduli space is considered. A simple, non-chiral, renormalizable model is presented to illustrate this mechanism. The well known, chiral, $SU(3) \times SU(2)$ model and its…
The all-loop anisotropic Thirring model interpolates between the WZW model and the non-Abelian T-dual of the anisotropic principal chiral model. We focus on the SU(2) case and we prove that it is classically integrable by providing its Lax…
We study integrable deformations of two-dimensional non-linear sigma-models and present a new class of classical solutions to critical bi-Yang-Baxter models for general groups. For the simplest example, namely the SL(2,R) bi-Yang-Baxter…
We proceed to study infinite-dimensional symmetries in two-dimensional squashed Wess-Zumino-Novikov-Witten (WZNW) models at the classical level. The target space is given by squashed S^3 and the isometry is SU(2)_L x U(1)_R. It is known…
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…
Spin-charge separation in pure SU(2) Yang-Mills theory was recently found to involve the dynamics of an O(3) non-linear sigma model and, seemingly, a Grassmannian non-linear sigma model. In this article we explicitly construct the…
We introduce a deformation of the Wess-Zumino-Novikov-Witten model with three-dimensional squashed sphere target space. We show how with an appropriate choice of Wess--Zumino and boundary terms it is possible to construct an infinite family…
Various aspects of non-linear sigma models with an $SU(N)\times U(1)$ symmetric target space are considered. In the case $N=2$, three-dimensional topological defects are discussed which are relevant for frustrated magnetic systems and which…
A novel classically integrable model is proposed. It is a deformation of the two-dimensional principal chiral model, embedded into a heterotic $\sigma$-model, by a particular heterotic gauge field. This is inspired by the bosonic part of…
We argue that two dimensional classical SU(2) Yang-Mills theory describes the embedding of Riemann surfaces in three dimensional curved manifolds. Specifically, the Yang-Mills field strength tensor computes the Riemannian curvature tensor…