Generalized KdV and quantum inverse scattering description of conformal minimal models

We propose an alternative description of two-dimensional conformal field theory in terms of quantum inverse scattering. It is based on the generalized KdV systems attached to A2(2), yielding the classical limit of Virasoro as Poisson bracket structure. The corresponding T-system is shown to coincide with the one recently proposed by Kuniba and Suzuki. We classify the primary operators of the minimal models that commute with all the integrals of motion, and that are therefore candidates to perturb the model by keeping the conservation laws. For our A2(2) structure these happen to be Φ1,2, Φ2,1, Φ1,5, in contrast to the A1(1) case, studied by Bazhanov, Lukyanov and Zamolodchikov [preprint CLNS 94/1316, RU-94-98, hep-th/9412229], related to Φ1,3.