Vortex driven phase transition in Topologically Massive QED

TL;DR

This paper investigates a vortex-driven phase transition in (2+1)-dimensional QED with a Chern-Simons term, showing how topological mass influences chiral symmetry breaking and employing Dyson-Schwinger equations for analysis.

Contribution

It demonstrates the existence of a vortex-driven phase transition in topologically massive QED and determines the critical topological mass for chiral condensate disappearance.

Findings

Critical topological mass is around 10^{-2} e^{2} for weak coupling.

Vortex solutions influence chiral symmetry breaking.

Chiral condensate is washed away above the critical mass.

Abstract

There is chiral like symmetry for 4-component massless fermion in (2+1)-dimensional gauge theory.Since QED$_{3}$ with Chern-Simons term contains vortex solution for vector potential,one may expect vortex driven phase transition as Kosterlitz-Thouless type where chiral condensate is washed away at zero temperature.To study this possibility,we evaluate the fermion propagator by Dyson-Schwinger equation numerically and spectral function analytically in the Landau gauge.For quenched case we adopt Ball-Chiu vertex to keep gauge invariance of the results.The critical value of topological mass,above which chiral condensate washed away, turned out to be $O(10^{-2})e^{2}$ at least for weak coupling in both cases.