Confinement in Maxwell-Chern-Simons Planar Quantum Electrodynamics and the 1/N approximation

TL;DR

This paper analyzes the fermion propagator in Maxwell-Chern-Simons planar QED, revealing a phase transition related to chiral symmetry and demonstrating charge screening across parameters using the 1/N approximation.

Contribution

It provides an analytical study of fermion mass generation and confinement in Maxwell-Chern-Simons QED using the 1/N approximation, highlighting phase transitions and parity effects.

Findings

First order phase transition at critical Chern-Simons coefficient

Parity-violating masses generated for all coefficients

Complete charge screening observed in the (N,θ)-plane

Abstract

We study the analytical structure of the fermion propagator in planar quantum electrodynamics coupled to a Chern-Simons term within a four-component spinor formalism. The dynamical generation of parity-preserving and parity-violating fermion mass terms is considered, through the solution of the corresponding Schwinger-Dyson equation for the fermion propagator at leading order of the 1/N approximation in Landau gauge. The theory undergoes a first order phase transition toward chiral symmetry restoration when the Chern-Simons coefficient $\theta$ reaches a critical value which depends upon the number of fermion families considered. Parity-violating masses, however, are generated for arbitrarily large values of the said coefficient. On the confinement scenario, complete charge screening --characteristic of the 1/N approximation-- is observed in the entire $(N,\theta)$-plane through the local and global properties of the vector part of the fermion propagator.