The Gauged Thirring Model

TL;DR

This paper introduces the gauged Thirring model as a gauge-invariant extension of the four-fermion interaction model, analyzing its phase structure, renormalization group flows, and potential for a nontrivial continuum limit in 3+1 dimensions.

Contribution

It proposes a gauge-invariant generalization of the Thirring model, explores its phase structure, and investigates conditions for a nontrivial continuum limit with renormalized coupling.

Findings

Nontrivial phase structure in 3+1 dimensions.

Evidence for a nontrivial continuum limit with large anomalous dimension.

Discussion of a perturbatively renormalizable extension.

Abstract

We propose the gauged Thirring model as a natural gauge-invariant generalization of the Thirring model, four-fermion interaction of current-current type. In the strong gauge-coupling limit, the gauged Thirring model reduces to the recently proposed reformulation of the Thirring model as a gauge theory. Especially, we pay attention to the effect coming from the kinetic term for the gauge boson field, which was originally the auxiliary field without the kinetic term. In 3 + 1 dimensions, we find the nontrivial phase structure for the gauged Thirring model, based on the Schwinger-Dyson equation for the fermion propagator as well as the gauge-invariant effective potential for the chiral order parameter. Within this approximation, we study the renormalization group flows (lines of constant physics) and find a signal for nontrivial continuum limit with nonvanishing renormalized coupling constant and large anomalous dimension for the gauged Thirring model in 3+1 dimensions, at least for small number of flavors $N_f$. Finally we discuss the (perturbatively) renormalizable extension of the gauged Thirring model.