Effective Action and Conformal Phase Transition in Three-Dimensional QED

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.