On Kinks and Bound States in the Gross-Neveu Model

TL;DR

This paper explicitly constructs kink and bound state solutions in the 2D Gross-Neveu model using supersymmetric quantum mechanics, providing a new method that could be applied to other field theories.

Contribution

It introduces a novel approach employing supersymmetric quantum mechanics to find static solutions in the Gross-Neveu model, avoiding inverse scattering techniques.

Findings

Derived explicit kink solutions in the unbroken supersymmetry sector.

Obtained DHN saddle point configurations in the broken supersymmetry sector.

Presented a method applicable to other two-dimensional field theories.

Abstract

We investigate static space dependent $\sigx=\lag\bar\psi\psi\rag$ saddle point configurations in the two dimensional Gross-Neveu model in the large N limit. We solve the saddle point condition for $\sigx$ explicitly by employing supersymmetric quantum mechanics and using simple properties of the diagonal resolvent of one dimensional Schr\"odinger operators rather than inverse scattering techniques. The resulting solutions in the sector of unbroken supersymmetry are the Callan-Coleman-Gross-Zee kink configurations. We thus provide a direct and clean construction of these kinks. In the sector of broken supersymmetry we derive the DHN saddle point configurations. Our method of finding such non-trivial static configurations may be applied also in other two dimensional field theories.