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

TL;DR

This study investigates how irrelevant four-fermion interactions influence dynamical mass generation and chiral symmetry breaking in ${ m QED}_3$, revealing a continuous dependence of the critical fermion number on weak symmetry-breaking interactions.

Contribution

It provides a renormalization group analysis showing the effect of irrelevant interactions on the critical fermion number in ${ m QED}_3$, including a gauge-invariant one-loop calculation.

Findings

Critical fermion number $N_c$ depends on weak chiral-symmetry-breaking interactions.

Pure ${ m QED}_3$ has a critical number $N_{c0} = 6$ for dynamical mass generation.

Chiral-symmetry-preserving mass cannot be generated in pure ${ m QED}_3$.

Abstract

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