W-infinity structure of the $sl(N)$ conformal affine Toda theories

Abstract

We reexamine the $W_{\infty }$ symmetry of the $sl(N)$ Conformal Affine Toda theories. It is shown that it is possible to reduce (nonuniquely) the zero curvature equation to a Lax equation for a first order pseudodifferential oprator, whose coefficients are the generators of the $W_{\infty }$ algebra. This clarifies the known relation between the Conformal Affine Toda theories and the KP hierarchy. A possible correspondence between the matrix models and the Conformal Affine Toda models is discussed.

13 pages

References in corpus (3)

• An alternative approach to KP hierarchy in matrix models
• Generalized W-algebras and Integrable Hierarchies
• A New Deformation of W-Infinity and Applications to the Two-loop WZNW and Conformal Affine Toda Models

Cited by in corpus (1)

• Affine opers and conformal affine Toda