Four Fermion Field Theories and the Chern-Simons Field: A Renormalization Group Study

TL;DR

This study investigates a (2+1)-dimensional fermionic model with Chern-Simons and four-fermion interactions, revealing how the stability of fixed points depends on the Chern-Simons parameter and N, using renormalization group analysis.

Contribution

It provides a non-perturbative analysis of a combined Chern-Simons and four-fermion model, identifying fixed point stability and ultraviolet behavior improvements with N.

Findings

Infrared stable fixed point at small Chern-Simons parameter

Transition to ultraviolet stability beyond a critical parameter value

Enhanced ultraviolet behavior of certain operators with increasing N

Abstract

In (2+1) dimensions, we consider the model of a $N$ flavor, two-component fermionic field interacting through a Chern-Simons field besides a four fermion self-interaction which consists of a linear combination of the Gross-Neveu and Thirring like terms. The four fermion interaction is not perturbatively renormalizable and the model is taken as an effective field theory in the region of low momenta. Using Zimmerman procedure for reducing coupling constants, it is verified that, for small values of the Chern-Simons parameter, the origin is an infrared stable fixed point but changes to ultraviolet stable as $\alpha$ becomes bigger than a critical $\alpha_c$. Composite operators are also analyzed and it is shown that a specific four fermion interaction has an improved ultraviolet behavior as $N$ increases.