Interacting fermions and domain wall defects in 2+1 dimensions

We consider a Dirac field in 2+1 dimensions with a domain wall like defect in its mass, minimally coupled to a dynamical Abelian vector field. The mass of the fermionic field is assumed to have just one linear domain wall, which is externally fixed and unaffected by the dynamics. We show that, under some general conditions on the parameters, the localized zero modes predicted by the Callan and Harvey mechanism are stable under the electromagnetic interaction of the fermions

Domain wall interactions due to vacuum Dirac field fluctuations in 2+1 dimensions

We evaluate quantum effects due to a $2$-component Dirac field in $2+1$ space-time dimensions, coupled to domain-wall like defects with a smooth shape. We show that those effects induce non trivial contributions to the (shape-dependent) energy of the domain walls. For a single defect, we study the divergences in the corresponding self-energy, and also consider the role of the massless zero mode, corresponding to the Callan-Harvey mechanism, by coupling the Dirac field to an external gauge field. For two defects, we show that the Dirac field induces a non trivial, Casimir-like effect between them, and provide an exact expression for that interaction in the case of two straight-line parallel defects. As is the case for the Casimir interaction energy, the result is finite and unambiguous.Comment: 17 pages, 1 figur