On dual description of 2D integrable sigma models

There exist several known examples of integrable deformations of 2D sigma models, which admit so-called dual description in terms of Toda-like theories. For such deformations we describe the system of screening charges depending on continuous parameter b, which defines the deformed sigma model in the limit b to infinity and a certain Toda QFT in the limit b to zero. In the sigma model regime it can be shown that the leading UV asymptotic of the deformed model coincides with a perturbed Gaussian theory. In the perturbative regime b to 0 one can see that the two-particle scattering matrix matches the expansion of the corresponding deformed sigma model trigonometric S-matrix. We illustrate the above description with the examples of O(N), OSp(N|2m) and other cases.