$\theta$ Effects in Chern-Simons ${\rm QED}_{2+1}$ with a Four-Fermi Interaction

TL;DR

This paper explores how the Chern-Simons coupling influences high-energy behavior in (2+1)-dimensional QED with a four-Fermi interaction, revealing that radiative corrections to the Chern-Simons term vanish at leading order.

Contribution

It provides a detailed analysis of the Chern-Simons effects on the critical four-Fermi coupling and the beta function using the 1/N expansion, showing no higher-order radiative corrections.

Findings

Radiative correction to the Chern-Simons coupling vanishes at O(1/N) in the broken phase.

No radiative corrections to the Chern-Simons term at higher orders in 1/N.

High-energy Green's functions behavior is characterized in the model.

Abstract

We investigate the effects of the Chern-Simons coupling on the high energy behavior in the $(2+1)$-dimensional Chern-Simons QED with a four-Fermi interaction. Using the $1/N$ expansion we discuss the Chern-Simons effects on the critical four-Fermi coupling at $O(1/N)$ and the $\beta$ function around it. High-energy behavior of Green's functions is also discussed. By explicit calculation, we find that the radiative correction to the Chern-Simons coupling vanishes at $O(1/N)$ in the broken phase of the dynamical parity symmetry. We argue that no radiative corrections to the Chern-Simons term arise at higher orders in the $1/N$ expansion.