Gauge invariant generalization of the 2D chiral Gross-Neveu model
W. Franzki, J. Jersák, R. Welters
Abstract
By means of the Lee-Shrock transformation we generalize the 2D Gross-Neveu (GN2) model to a U(1) gauge theory with charged fermion and scalar fields in 2D (χU ϕ2 model). The χU ϕ2 model is equivalent to the GN2 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 XY2 model phase transition at weak coupling. This suggests that the χU ϕ2 model is in the same universality class as the GN2 model and thus renormalizable.
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