LAUSR

In this paper we present a general framework to construct integrable Z22-graded extensions of classical, two-dimensional Toda and conformal affine Toda theories. The scheme is applied to define the extended Liouville and Sinh–Gordon models; they are based on Z22-graded color Lie algebras and their fields satisfy a parabosonic statistics. The mathematical tools here introduced are the Z22-graded covariant extensions of the Lax pair formalism and of the Polyakov’s soldering procedure. The Z22-graded Sinh–Gordon model is derived from an affine Z22-graded color Lie algebra, mimicking a procedure originally introduced by Babelon-Bonora to derive the ordinary Sinh–Gordon model. The color Lie algebras under considerations are: the 6-generator Z22-graded sl2, the Z22-graded affine sl2^ algebra with two central extensions, the Z22-graded Virasoro algebra obtained from a Hamiltonian reduction.