From integrability to conformal symmetry: bosonic superconformal Toda theories

The author studies the new conformal integrable models obtained from conformal reductions of WZNW theory associated with second order constraints, these models are called bosonic superconformal Toda models due to their conformal spectra and their resemblance to the usual Toda theories. From the reduction procedure the equations of motion and the linearized Lax equations for such systems in a generic gradation of the underlying Lie algebra are obtained. Then, in the special case of principal gradation, the author derives the classical r-matrix, fundamental Poisson relation, exchange algebra of the chiral operators and finds out the classical vertex operators. The result shows that the author's model may play a similar role with respect to the ordinary Toda theories in which one may obtain various conformal properties of the model from its integrability