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

TL;DR

This paper extends the 2D Gross-Neveu model to include gauge interactions, demonstrating that key features like mass generation and asymptotic freedom persist at finite coupling, indicating universality and renormalizability.

Contribution

The authors introduce a gauge-invariant generalization of the 2D Gross-Neveu model using the Lee-Shrock transformation, showing its equivalence at infinite coupling and persistence of key phenomena at finite coupling.

Findings

Dynamical fermion mass generation persists at finite gauge coupling.

Asymptotic freedom remains in the effective four-fermion coupling.

The model shares universality class with the original GN$_2$ model.

Abstract

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 ($\chi U \phi_2$ model). The $\chi U \phi_2$ 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 $\chi U \phi_2$ model is in the same universality class as the GN$_2$ model and thus renormalizable.