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arXiv · hep-th/9312045

Generalized NLS Hierarchies from Rational $W$ Algebras

Francesco Toppan
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Abstract

Finite rational $\cw$ algebras are very natural structures appearing in coset constructions when a Kac-Moody subalgebra is factored out. In this letter we address the problem of relating these algebras to integrable hierarchies of equations, by showing how to associate to a rational $\cw$ algebra its corresponding hierarchy. We work out two examples: the $sl(2)/U(1)$ coset, leading to the Non-Linear Schrödinger hierarchy, and the $U(1)$ coset of the Polyakov-Bershadsky $\cw$ algebra, leading to a $3$-field representation of the KP hierarchy already encountered in the literature. In such examples a rational algebra appears as algebra of constraints when reducing a KP hierarchy to a finite field representation. This fact arises the natural question whether rational algebras are always associated to such reductions and whether a classification of rational algebras can lead to a classification of the integrable hierarchies.

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Francesco Toppan. 1993-12-07. Generalized NLS Hierarchies from Rational $W$ Algebras. https://doi.org/10.1016/0370-2693(94)90725-0

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