Critical number of flavors in QED

We demonstrate that in unquenched quantum electrodynamics (QED), chiral symmetry breaking ceases to exist above a critical number of fermion flavors Nf. This is a necessary and sufficient consequence of the fact that there exists a critical value of electromagnetic coupling α beyond which dynamical mass generation gets triggered. We employ a multiplicatively renormalizable photon propagator involving leading logarithms to all orders in α to illustrate this. We study the flavor and coupling dependence of the dynamically generated mass analytically as well as numerically. We also derive the scaling laws for the dynamical mass as a function of α and N f. Up to a multiplicative constant, these scaling laws are related through (α,αc)↔(1/Nf,1/Nfc). Calculation of the mass anomalous dimension γm shows that it is always greater than its value in the quenched case. We also evaluate the β function. The criticality plane is drawn in the (α,Nf) phase space which clearly depicts how larger Nf is required to restore chiral symmetry for an increasing interaction strength. © 2011 American Physical Society.