Chiral symmetry breaking in ${QED}_{3}$ in presence of irrelevant interactions: a renormalization group study

Motivated by recent theoretical approaches to high temperature superconductivity, we study dynamical mass generation in three dimensional quantum electrodynamics (${QED}_{3}$) in 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 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 ${QED} _3$. We also find that chiral-symmetry-preserving mass cannot become dynamically generated in pure ${QED}_{3}$.