Dynamical Flavor Symmetry Breaking by a Magnetic Field in \(2+1\) Dimensions

Abstract

It is shown that in \(2+1\) dimensions, a constant magnetic field is a strong catalyst of dynamical flavor symmetry breaking, leading to generating a fermion dynamical mass even at the weakest attractive interaction between fermions. The essence of this effect is that in a magnetic field, in \(2+1\) dimensions, the dynamics of fermion pairing is essentially one-dimensional. The effect is illustrated in the Nambu-Jona-Lasinio model in a magnetic field. The low-energy effective action in this model is derived and the thermodynamic properties of the model are considered. The relevance of this effect for planar condensed matter systems and for \(3+1\) dimensional theories at high temperature is pointed out.