Algebraic aspects of the deformation of conformal field theory

We point out that the Toda lattice hierarchy known in soliton theory is relevant for the description of the deformation of rational conformal field theories while the KP hierarchy describes unperturbed conformal field theories. In particular, the holomorphic parts of the conserved currents in the perturbed system (the Toda lattice hierarchy) coincide with the conserved currents in the KP hierarchy and can be written in terms of the W-algebraic currents. Furthermore, their anti-holomorphic counterparts are obtained. These results assure the conjecture that Toda field theory associated with an affine Lie algebra g describes the system perturbed from g coset conformal model. (author)