Gauge invariant generalization of the 2D chiral Gross-Neveu model

By means of the Lee-Shrock transformation we generalize the 2D Gross-Neveu (GN${}_2$) model to a U(1) gauge theory with charged fermion and scalar fields in 2D ($\chi U{\varphi }_2$ model). The $\chi U{\varphi }_2$ model is equivalent to the GN${}_2$ model at infinite gauge coupling. We show that the dynamical fermion mass generation and asymptotic freedom in the effective four-fermion coupling persist also when the gauge coupling decreases. These phenomena are not influenced by the XY${}_2$ model phase transition at weak coupling. This suggests that the $\chi U{\varphi }_2$ model is in the same universality class as the GN${}_2$ model and thus renormalizable.