Boundary Effects in the Magnetic Catalysis of Chiral Symmetry Breaking

The catalysis of chiral symmetry breaking by an applied constant magnetic field and in the presence of boundaries along third axis is investigated in the four-dimensional Nambu-Jona-Lasinio model. It is shown that in case of periodic boundary conditions for fermions the magnetic field breaks the chiral symmetry, generating a dynamical mass even at the weakest attractive interaction between fermions. For antiperiodic boundary conditions the effect of the finite third dimension is to counteract the chiral symmetry breaking.