Two-dimensional model of dynamical fermion mass generation in strongly coupled gauge theories

Abstract

We generalize the $N_F=2$ Schwinger model on the lattice by adding a charged scalar field. In this so-called $χUϕ_2$ model the scalar field shields the fermion charge, and a neutral fermion, acquiring mass dynamically, is present in the spectrum. We study numerically the mass of this fermion at various large fixed values of the gauge coupling by varying the effective four-fermion coupling, and find an indication that its scaling behavior is the same as that of the fermion mass in the chiral Gross-Neveu model. This suggests that the $χUϕ_2$ model is in the same universality class as the Gross-Neveu model, and thus renormalizable and asymptotic free at arbitrary strong gauge coupling.