Effective Action and Conformal Phase Transition in Three-Dimensional QED

TL;DR

This paper analyzes the phase transition in three-dimensional QED using the effective action for composite operators, revealing a conformal phase transition characterized by an abrupt change in light excitations despite being continuous.

Contribution

It demonstrates that the phase transition in QED3 at a critical number of fermion flavors is a conformal phase transition with unique spectral and symmetry features.

Findings

Continuous phase transition at N_f=N_cr with abrupt spectrum change

Effective potential calculated in leading order of 1/N_f

Connection discussed between QED3 dynamics and QCD4

Abstract

The effective action for local composite operators in $QED_3$ is considered. The effective potential is calculated in leading order in $1/N_f$ ($N_f$ is the number of fermion flavors) and used to describe the features of the phase transition at $N_f=N_{\rm cr}$, $3<N_{\rm cr}<5$. It is shown that this continuous phase transition satisfies the criteria of the conformal phase transition, considered recently in the literature. In particular, there is an abrupt change of the spectrum of light excitations at the critical point, although the phase transition is continuous, and the structure of the equation for the divergence of the dilatation current is essentially different in the symmetric and nonsymmetric phases. The connection of this dynamics with the dynamics in $QCD_4$ is briefly discussed.