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

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

1993-03-08

arxiv.org/abs/hep-th/9303045v1

Phys.Lett. B309 (1993) 297-303

Physics

High Energy Physics

High Energy Physics - Theory

13 pages

Scientific paper

10.1016/0370-2693(93)90937-D

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.

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