Critical Number of Flavours in QED

TL;DR

This paper investigates the critical number of fermion flavours in unquenched QED, demonstrating how chiral symmetry breaking depends on the electromagnetic coupling and identifying the conditions under which it ceases to exist.

Contribution

It introduces a detailed analysis of the flavour and coupling dependence of dynamical mass generation in unquenched QED, including new scaling laws and the phase diagram in the (lpha, N_f) space.

Findings

Chiral symmetry breaking ceases above a critical N_f.

Scaling laws relate mass, lpha, and N_f.

The criticality phase diagram shows how N_f influences symmetry restoration.

Abstract

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 $\alpha$ beyond which dynamical mass generation gets triggered. We employ a multiplicatively renormalizable photon propagator involving leading logarithms to all orders in $\alpha$ 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 $\alpha$ and $N_f$. Up to a multiplicative constant, these scaling laws are related through $(\alpha, \alpha_c) \leftrightarrow (1/N_f, 1/N_f^c)$. Calculation of the mass anomalous dimension $\gamma_m$ shows that it is always greater than its value in the quenched case. We also evaluate the $\beta$-function. The criticality plane is drawn in the $(\alpha,N_f)$ phase space which clearly depicts how larger $N_f$ is required to restore chiral symmetry for an increasing interaction strength.