Interacting fermions and domain wall defects in 2+1 dimensions

TL;DR

This paper studies a 2+1 dimensional Dirac fermion with a domain wall mass defect coupled to a dynamical gauge field, demonstrating the stability of localized zero modes under electromagnetic interactions.

Contribution

It extends the Callan-Harvey mechanism to include dynamical gauge fields, showing zero mode stability in this context.

Findings

Zero modes are stable under electromagnetic interactions.

The model demonstrates robustness of domain wall localized states.

Conditions for stability are identified.

Abstract

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.