The sigma model (dual) representation for a two-parameter family of integrable quantum field theories

We introduce and study two-parameter families of integrable field theories. The perturbative and non-perturbative methods are used to justify their factorized scattering theory in the form of the direct products of two S-matrices of the sine-Gordon model. The Bethe ansatz technique is applied for the calculation of the observables in the strong coupling region. The results are in the exact agreement with ones following from the sigma model action which is a two-parameter U(1) x U(1) symmetrical deformation of the O(4) non-linear sigma model. The application of the sigma model representation to related perturbed conformal field theories is discussed.