  We introduce and study conformal field theories specified by $W-$algebras
commuting with certain set of screening charges. These CFT's possess
perturbations which define integrable QFT's. We establish that these QFT's have
local and non-local Integrals of Motion and admit the perturbation theory in
the weak coupling region. We construct factorized scattering theory which is
consistent with non-local Integrals of Motion and perturbation theory. In the
strong coupling limit the $S-$matrix of this QFT tends to the scattering matrix
of the $O(N)$ sigma model. The perturbation theory, Bethe anzatz technique,
renormalization group approach and methods of conformal field theory are
applied to show, that the constructed QFT's are dual to integrable deformation
of $O(N)$ sigma-models.
