On the critical behavior of (2+1)-dimensional QED

TL;DR

This paper analyzes the critical behavior of (2+1)-dimensional QED, showing how the range of fermion flavors for dynamical mass generation depends on gauge choice and order of expansion, highlighting gauge sensitivity.

Contribution

It extends previous analysis of (2+1)D QED by including next-to-leading order effects in the 1/N expansion, revealing gauge-dependent critical N values for chiral symmetry breaking.

Findings

Dynamical fermion mass exists for N<3.78 in Landau gauge.

In Feynman gauge, dynamical mass is absent.

Critical N decreases with higher-order corrections.

Abstract

It is shown the analysis [1] for QED in 2+1 dimensions with N four-component fermions in the leading and next-to-leading orders of the 1/N expansion. As it was demonstrated in [1] the range of the admissible values N, where the dynamical fermion mass exist, decreases strongly with the increasing of the gauge charge. So, in Landau gauge the dynamical chiral symmetry breaking appears for N<3.78, that is very close to the results of the leading order and in Feynman gauge dynamical mass is completely absent.