No Primordial Magnetic Field from Domain Walls

Abstract

It is pointed out that, contrary to some claims in the literature, the domain walls cannot be a source of a correlated at large scales primordial magnetic field, even if the fermionic modes bound on the wall had ferromagnetic properties. In a particular model with massive (2+1) dimensional fermions bound to a domain wall, previously claimed to exhibit a ferromagnetic behavior, it is explicitly shown that the fermionic system in fact has properties of a normal diamagnetic with the susceptibility vanishing at high temperature.