Nonlinear realizations of $W_3$ symmetry

Abstract

We deduce the $s{l}_3$ Toda realization of classical $W_3$ symmetry on two scalar fields in a geometric way, proceeding from a nonlinear realization of some associate higher-spin symmetry $W_3^{\infty }$. The Toda equations are recognized as the constraints singling out a two-dimensional fully geodesic subspace in the initial coset space of $W_3^{\infty }$. The proposed geometric approach can be extended to other nonlinear algebras and integrable systems.

8 pages

References in corpus (1)

• Geometry and W-Gravity

Cited by in corpus (3)

• Superfield Realizations of $N=2$ Super-$W_3$
• Nonlinear Realizations of the $W_3^{(2)}$ Algebra
• Multi-Field Coset Space Realizations of $w_{1+\infty }$