Two-dimensional nonlinear fermionic models in curved space with torsion

Abstract

A completely integrable two-dimensional model of gravity with dynamical metric and torsion coupled to 2D massless Dirac matter is extended by inclusion of a nonlinear fermionic interaction. The classical equations of motion of this model are solved by considering perturbations up to second order. The Green function for the massless Dirac equation in this model is also calculated.