Critical Number of Flavours in QED

We demonstrate that in unquenched quantum electrodynamics (QED), chiral symmetry breaking ceases to exist above a critical number of fermion flavours $N_f$. 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 flavour 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 $(α, α_c) \leftrightarrow (1/N_f, 1/N_f^c)$. Calculation of the mass anomalous dimension $γ_m$ 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 $(α,N_f)$ phase space which clearly depicts how larger $N_f$ is required to restore chiral symmetry for an increasing interaction strength.

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