Fermion zero modes in N=2 supervortices

TL;DR

This paper investigates fermionic zero modes in N=2 supersymmetric vortices, revealing new modes with unique mass properties that challenge existing index theorems and expand understanding of vortex fermion spectra.

Contribution

It identifies new fermionic zero modes in semilocal vortices with non-winding scalar fields, clarifying their mass relations and implications for index theorem applications.

Findings

Discovery of new zero modes with opposite chirality.

Zero modes acquire mass from Yukawa couplings to non-winding scalars.

These modes evade traditional index theorems counting total zero modes.

Abstract

We study the fermionic zero modes of BPS semilocal magnetic vortices in N=2 supersymmetric QED with a Fayet-Iliopoulos term and two matter hypermultiplets of opposite charge. There is a one-parameter family of vortices with arbitrarily wide magnetic cores. Contrary to the situation in pure Nielsen-Olesen vortices, new zero modes are found which get their masses from Yukawa couplings to scalar fields that do not wind and are non-zero at the core. We clarify the relation between fermion mass and zero modes. The new zero modes have opposite chiralities and therefore do not affect the net counting (left minus right) of zero modes coming from index theorems but manage to evade other index theorems in the literature that count the total number (left plus right) of zero modes in simpler systems.