Instantons of two-dimensional fermionic effective actions by inverse scattering transformation (Q1076916)

A method to find symmetric solutions of the nonlinear and nonlocal saddle-point equations for the effective actions, containing the logarithm of a functional Dirac determinant, which appear in 1/N expansions of fermionic theories is proposed. This method consists in using the scattering data of the rotationally symmetric Dirac equation in two dimensions with the angular momentum as a spectral parameter. The method is applied to fermionic models with quartic coupling. It is shown that the effective action that generates the 1/N expansion admits a closed form in terms of the scattering data only in the particular case of Gross-Neveu and Chiral Gross-Neveu models. No instanton solutions are present in these two models. This fact suggested that the 1/N expansion could be convergent.