Dynamical Effects of Chern-Simons Term

TL;DR

This paper investigates how the Chern-Simons term influences fermion mass generation in 2+1D QED, revealing that it causes a split in fermion masses and affects the critical number of flavors needed for mass generation.

Contribution

It demonstrates the impact of the Chern-Simons term on dynamical fermion mass generation and the critical flavor number in 2+1D QED within a large N expansion framework.

Findings

Half of the fermions acquire mass M+m, the other half M-m.

Parity-preserving mass m is generated only when N<N_c.

The Chern-Simons term reduces both the critical N and the mass m.

Abstract

We study how the Chern-Simons term effects the dynamically generated fermion mass in $(2+1)D$ Quantum Electrodynamics in the framework of large $N$ expansion. We find that when the Chern-Simons term is present half of the fermions get mass $M+m$ and half get $M-m$. The parity-preserving mass $m$ is generated only when $N<\tilde{N}_c$. Both the critical number, $\tilde{N}_c$, of fermion flavor and the magnitude, $m$, reduce when the effect of the Chern-Simons term dominates.