Chiral symmetry breaking in three-dimensional quantum electrodynamics as fixed point annihilation

TL;DR

This paper investigates chiral symmetry breaking in three-dimensional quantum electrodynamics, modeling it as a fixed point annihilation process, and estimates the critical number of fermions for the phase transition.

Contribution

It provides a theoretical framework linking fixed point annihilation to chiral symmetry breaking and estimates the critical fermion number in three dimensions.

Findings

Estimated critical fermion number N_c ≈ 2.89 in 3D.

Showed N_c approaches zero as dimension approaches four.

Discussed phase boundary features in (d,N) plane.

Abstract

Spontaneous chiral symmetry breaking in three dimensional ($d=3$) quantum electrodynamics is understood as annihilation of an infrared-stable fixed point that describes the large-N conformal phase by another unstable fixed point at a critical number of fermions $N=N_c$. We discuss the root of universality of $N_c$ in this picture, together with some features of the phase boundary in the $(d,N)$ plane. In particular, it is shown that as $d\rightarrow 4$, $N_c\rightarrow 0$ with a constant slope, our best estimate of which suggests that $N_c = 2.89$ in $d=3$.