RG analysis of magnetic catalysis in Dynamical symmetry breaking

TL;DR

This paper uses renormalization group analysis to demonstrate that a strong external magnetic field induces dynamical symmetry breaking in fermionic systems, regardless of the initial four-Fermi interaction or electromagnetic coupling strength.

Contribution

It provides a detailed RG analysis showing magnetic catalysis of symmetry breaking, including cases without four-Fermi interactions and arbitrary electromagnetic couplings.

Findings

Any attractive four-Fermi interaction becomes strong at low energies.

Magnetic field induces Landau energy gap leading to symmetry breaking.

Dynamical symmetry breaking occurs for any electromagnetic coupling.

Abstract

We perform the renormalization group analysis on the dynamical symmetry breaking under strong external magnetic field, studied recently by Gusynin, Miransky and Shovkovy. We find that any attractive four-Fermi interaction becomes strong in the low energy, thus leading to dynamical symmetry breaking. When the four-Fermi interaction is absent, the $\beta$-function for the electromagnetic coupling vanishes in the leading order in $1/N$. By solving the Schwinger-Dyson equation for the fermion propagator, we show that in $1/N$ expansion, for any electromagnetic coupling, dynamical symmetry breaking occurs due to the presence of Landau energy gap by the external magnetic field.