Domain Wall in Nambu-Jona-Lasinio Model

TL;DR

This paper investigates the properties of domain walls in the Nambu-Jona-Lasinio model, solving the Jackiw-Rebbi problem and analyzing bound states, with implications for understanding QCD vacuum structures.

Contribution

It provides an explicit solution to the Jackiw-Rebbi problem in the NJL model and explores the conditions for bound states at domain walls.

Findings

No bound states at the domain wall under current assumptions

Higher-order corrections could induce bound states

Potential for using bound states as tests for QCD features

Abstract

The approximation for the NJL gap equation that was developed in our previous paper allows us to investigate vacuum inhomogeneities in the mean field approach. The simplest case of a domain wall is studied thoroughly. The Jackiw-Rebbi problem which arises in treatment of the fermions' interaction with the domain wall is solved explicitly and the entire spectrum of bound states is described. It is estabilished that under our assumptions no bound states exist at the domain wall, however higher-order corrections may make them appear. Thus existence of the quark bound states at domain walls may be a good test for subtle features of QCD.