相关论文: Nonlinear realizations of $W_3$ symmetry

In this letter we consider the nonlinear realizations of the classical Polyakov's algebra $W_3^{(2)}$. The coset space method and the covariant reduction procedure allow us to deduce the Boussinesq equation with interchanged space and…

We construct new coset realizations of infinite-dimensional linear $W_3^{\infty}$ symmetry associated with Zamolodchikov's $W_3$ algebra which are different from the previously explored $sl_3$ Toda realization of $W_3^{\infty}$. We deduce…

We consider the two-dimensional $\mathfrak{sl}_n$ quantum Toda field theory with an imaginary background charge. This conformal field theory has a higher spin symmetry ($W_n$ algebra), a central charge $c \leq n-1$ and a continuous…

For all non-symmetric discrete relativistic Toda type equations we establish a relation to 3D consistent systems of quad-equations. Unlike the more simple and better understood symmetric case, here the three coordinate planes of $\mathbb…

We extend the coset space formulation of the one-field realization of $w_{1+\infty}$ to include more fields as the coset parameters. This can be done either by choosing a smaller stability subalgebra in the nonlinear realization of…

This article is the first of a two-part series dedicated to studying the symmetries enjoyed by the probabilistic construction of the $\mathfrak{sl}_3$ boundary Toda Conformal Field Theory. Namely in the present document we show that this…

In analogy with the Liouville case we study the $sl_3$ Toda theory on the lattice and define the relevant quadratic algebra and out of it we recover the discrete $W_3$ algebra. We define an integrable system with respect to the latter and…

We consider the nonlinear algebras $W(sl(4),sl(3))$ and $W(sl(3|1),sl(3))$ and find their realizations in terms of currents spanning conformal linearizing algebras. The specific structure of these algebras, allows us to construct…

The symmetries of the simplest non-abelian Toda equations are discussed. The set of characteristic integrals whose Hamiltonian counterparts form a W-algebra, is presented.

The present paper describes the $W$--geometry of the Abelian finite non-periodic (conformal) Toda systems associated with the $B,C$ and $D$ series of the simple Lie algebras endowed with the canonical gradation. The principal tool here is a…

Toda conformal field theories are natural generalizations of Liouville conformal field theory that enjoy an enhanced level of symmetry. In Toda conformal field theories this higher-spin symmetry can be made explicit, thanks to a path…

We obtain a new free field realization of $N=2$ super $W_{3}$ algebra using the technique of quantum hamiltonian reduction. The construction is based on a particular choice of the simple root system of the affine Lie superalgebra…

We study classical $N=2$ super-$W_3$ algebra and its interplay with $N=2$ supersymmetric extensions of the Boussinesq equation in the framework of the nonlinear realization method and the inverse Higgs - covariant reduction approach. These…

The nonlinear scalar-field realisation of $w_{1+\infty}$ symmetry in $d=2$ dimensions is studied in analogy to the nonlinear realisation of $d=4$ conformal symmetry $SO(4,2)$. The $w_{1+\infty}$ realisation is derived from a coset-space…

On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.

We discuss the emergence of W-algebras as asymptotic symmetries of higher-spin gauge theories coupled to three-dimensional Einstein gravity with a negative cosmological constant. We focus on models involving a finite number of bosonic…

The fact that certain non-linear $W_{2,s}$ algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize $W_{2,s}$ algebras from linear $W_{1,2,s}$ algebras. In this paper, we first construct the…

We construct a new class of positive solutions for a classical semilinear elliptic problem in the plane which arise for instance as the standing-wave problem for the standard nonlinear Schr\"odinger equation or in nonlinear models in…

We obtain exhaustive classification of inequivalent realizations of the Witt and Virasoro algebras by Lie vector fields of differential operators in the space $\mathbb{R}^3$. Using this classification we describe all inequivalent…

For the proposed duality relating a family of N=4 superconformal coset models to a certain supersymmetric higher spin theory on AdS_3, the asymptotic symmetry algebra of the bulk description is determined. It is shown that, depending on the…