Chiral symmetry breaking in three-dimensional quantum electrodynamics in the presence of irrelevant interactions: A renormalization group study

Abstract

Motivated by recent theoretical approaches to high temperature superconductivity, we study dynamical mass generation in three-dimensional quantum electrodynamics $({\mathrm{QED}}_{3})$ in the presence of irrelevant four-fermion quartic terms. The problem is reformulated in terms of the renormalization group flows of certain four-fermion couplings and charge, and then studied in the limit of a large number of fermion flavors $N$. We find that the critical number of fermions ${N}_{c}$ below which the mass becomes dynamically generated depends continuously on a weak chiral symmetry breaking interaction. One-loop calculation in our gauge-invariant approach yields ${N}_{c0}=6$ in pure ${\mathrm{QED}}_{3}$. We also find that chiral symmetry preserving mass cannot become dynamically generated in pure ${\mathrm{QED}}_{3}$.