Interacting fermions and domain wall defects in 2+1 dimensions

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.

New developments in the quantization of supersymmetric solitons (kinks, vortices and monopoles)

“…[55], it was claimed that the usual multiplet shortening arguments in favor of BPS saturation would not be applicable to the N = 2 vortex since in the vortex background there would be two rather than one fermionic zero modes [58], leading to two short multiplets which have the same number of states as one long multiplet. 8 We showed however that the extra zero mode postulated in [55] has to be discarded because its gaugino component is singular, and that only after doing so there is agreement with the results from index theorems [59,58,60]. For this reason, standard multiplet shortening arguments do apply, explaining the BPS saturation at the quantum level that we observe in our explicit one-loop calculations.…”

“…This seems to doom the prospects of anomalies in Z, because we already mentioned that there are no anomalies in the translational symmetry. However, the presence of the soliton in the background polarizes the fermionic excitations in the extra dimensions [7,8]. This phenomenon has the same origin as the quantum Hall effect, and as a result the left-moving and the right-moving modes of the fermions have different normalizations on the domain wall created by the soliton.…”