Boundary Effects in the Magnetic Catalysis of Chiral Symmetry Breaking

TL;DR

This paper studies how boundaries and magnetic fields influence chiral symmetry breaking in a four-dimensional model, revealing that boundary conditions significantly affect whether symmetry is broken or restored.

Contribution

It demonstrates the impact of boundary conditions on magnetic catalysis of chiral symmetry breaking within the Nambu-Jona-Lasinio model.

Findings

Periodic boundaries induce symmetry breaking via magnetic catalysis.

Antiperiodic boundaries suppress chiral symmetry breaking.

Magnetic field can generate dynamical mass at weak interactions.

Abstract

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.