Induced magnetic moments in three-dimensional gauge theories with external magnetic fields

We study the appearance of induced parity-violating magnetic moment, in the presence of external magnetic fields, for even-number of fermion species coupled to dynamical fields in three dimensions. Specifically, we use a SU(2) × U(1) gauge model for dynamical gauge symmetry breaking, which has also been proposed recently as a field theorerical model for high-Tc superconductors. By decomposing the fermionic degrees of freedom in terms of Landau levels, we show that, in the effective theory with the lowest Landau levels, a parity-violating magnetic moment interaction is induced by the higher Landau levels when the fermions are massive. The possible relevance of this result for a recently observed phenomenon in high-Tc superconductors is also discussed.