Fermion number of twisted kinks in the NJL$_2$ model, revisited

TL;DR

This paper revisits the fermion number of twisted kinks in the NJL$_2$ model, proposing a finite box regularization method that preserves integrability and allows consistent fermion number assignment at any twist angle.

Contribution

It introduces a finite box regularization for twisted kinks in the NJL$_2$ model, providing a simpler and more general approach compared to previous methods.

Findings

Finite box regularization preserves integrability.

Consistent fermion number assignment for all twist angles.

Simplifies analysis over previous infrared regularization methods.

Abstract

As a consequence of axial current conservation, fermions cannot be localized in the massless NJL$_2$ model. In the case of twisted kinks, this manifests itself in a cancellation between valence fermion density and fermion density induced in the Dirac sea. To attribute the correct fermion number to these bound states requires an infrared regularization. Recently, this has been achieved by introducing a bare fermion mass, at least in the non-relativistic regime of small twist angles and fermion numbers. Here, we propose a simpler regularization by a finite box which preserves integrability and can be applied at any twist angle. A consistent and physically plausible assignment of fermion number to all twisted kinks emerges.