Gauge covariant solution for the Schwinger-Dyson equation in three-dimensional QED with Chern-Simons term

TL;DR

This paper develops a gauge covariant approach to solving the Schwinger-Dyson equation in three-dimensional QED with a Chern-Simons term, revealing gauge dependence in phase boundaries related to symmetry breaking.

Contribution

It introduces a gauge covariant solution using the Ball-Chiu vertex to improve the Schwinger-Dyson equation analysis in 3D QED with Chern-Simons term.

Findings

Demonstrates gauge dependence of phase boundary for symmetry breaking.

Provides numerical solutions to the Schwinger-Dyson equation with improved vertex function.

Highlights the impact of gauge choice on phase transition analysis.

Abstract

An Abelian gauge theory with Chern-Simons term is investigated for a four-component Dirac fermion in 1+2 dimensions. The Ball-Chiu (BC) vertex function is employed to modify the rainbow-ladder approximation for the Schwinger-Dyson (SD) equation. We numerically solve the SD equation and show the gauge dependence for the resulting phase boundary for the parity and the chiral symmetry.