RG ANALYSIS OF MAGNETIC CATALYSIS IN DYNAMICAL SYMMETRY-BREAKING

We perform the renormalization group analysis on dynamical symmetry br eaking under a strong external magnetic field studied recently by Gusy nin, Miransky, and Shovkovy. We find that any attractive four-Fermi in teraction becomes strong at low energy, thus leading to dynamical symm etry breaking. When the four-Fermi interaction is absent, the beta fun ction for the electromagnetic coupling vanishes in the leading order i n 1/N. By solving the Schwinger-Dyson equation for the fermion propaga tor, we show that in the 1/N expansion, for any electromagnetic coupli ng, dynamical symmetry breaking occurs due to the presence of a Landau energy gap by the external magnetic field.