Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups

Details Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups

1996-05-28

arxiv.org/abs/hep-th/9605193v1

Phys.Lett. B387 (1996) 759-768

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, LaTeX

Scientific paper

10.1016/0370-2693(96)01106-9

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 establish the relation with the Toda lattice hierarchy. We compute the the relevant continuum limits. Finally we find the quantum version of the quadratic algebra.

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