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

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.

6 pages, 4 figures; v2: minor corrections

References in corpus (5)

• Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems
• Self-consistent multiple complex-kink solutions in Bogoliubov-de Gennes and chiral Gross-Neveu systems
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Cited by in corpus (1)

• Twisted kink dynamics in multiflavor chiral Gross-Neveu model