Critical number of fermions in three-dimensional QED

TL;DR

This paper refines the critical number of fermions in 2+1 dimensional QED, showing that chiral symmetry breaking occurs for N less than approximately 2.85, using Dyson-Schwinger equations for more accurate results.

Contribution

The study provides a more precise, gauge-independent estimate of the critical fermion number in QED3 by solving Dyson-Schwinger equations, improving upon previous analytical approximations.

Findings

Critical fermion number N_c ≈ 2.85

Chiral symmetry breaking occurs for N < N_c

Estimate of chiral condensate for N=2

Abstract

Previous analytical studies of quantum electrodynamics in $2+1$ dimensions (QED3) have shown the existence of a critical number of fermions for onset of chiral symmetry breaking, the most known being the value $N_c\approx3.28$ obtained by Nash to $1/N^2$ order in the $1/N$ expansion [16]. This analysis is reconsidered by solving the Dyson-Schwinger equations for the fermion propagator and the vertex to show that the more accurate gauge independent value is $N_c\approx2.85$, and for $N<N_c$ the chiral symmetry is dynamically broken. An estimate for the value of chiral condensate $\langle\bar\psi\psi\rangle$ is given for $N=2$. Knowing precise $N_c$ would be important for comparison between continuum studies and lattice simulations of QED3.