Critical Behavior of (2 + 1)-Dimensional QED: 1/N Expansion

Anatoly V Kotikov,Sofian Teber

doi:10.3390/particles3020026

Abstract

We present recent results on dynamical chiral symmetry breaking in (2 + 1)-dimensional QED with N four-component fermions. The results of the 1 / N expansion in the leading and next-to-leading orders were found exactly in an arbitrary nonlocal gauge.

Highlights

We present in a self-contained way the results of Refs. [1,2], where the critical behavior of Quantum Electrodynamics in 2 + 1 dimensions (QED3) have been studied
Contrary to previous reports [3,4,5], we here follow the Addendum of Ref. [2], which contains a strong upgrade of the exact results of [2] thereby proving the complete gauge-independence of the value of the critical fermion number, Nc, which is such that dynamical chiral symmetry breaking (DχSB) in QED3 takes place only for N < Nc
We have presented a study of DχSB in QED3, including an exact computation of 1/N2 corrections to the SD equation and considering the full ξ-dependence of the gap equation

Summary

Introduction

We present in a self-contained way the results of Refs. [1,2], where the critical behavior of Quantum Electrodynamics in 2 + 1 dimensions (QED3) have been studied. [2], which contains a strong upgrade of the exact results of [2] thereby proving the complete gauge-independence of the value of the critical fermion number, Nc, which is such that dynamical chiral symmetry breaking (DχSB) in QED3 takes place only for N < Nc. following Ref. The purpose of this paper is to present the main arguments of the papers [1,2] (and corresponding Addendum and Erratum, respectively) leading to exact DχSB results in arbitrary nonlocal gauge [36,37] This achievement represents a significant improvement in terms of the approximate Nash NLO results that were made mostly in the Feynman gauge. After resummation of the renormalization constant of the wave function, we find that the LO and NLO terms in the gap equation become gauge-invariant and match the results of [29]

SD Equations

NLO Now consider the NLO contributions that can be parameterized as

Extraction of the Most “Important” Terms

Gap Equation

Resummation

Conclusions