On Kinks and Bound States in the Gross-Neveu Model

Details On Kinks and Bound States in the Gross-Neveu Model On Kinks and Bound States in the Gross-Neveu Model

1994-08-22

arxiv.org/abs/hep-th/9408120v2

Phys.Rev. D51 (1995) 4503-4511

Physics

High Energy Physics

High Energy Physics - Theory

Revised version. A new section added with derivation of the DHN static configurations in the sector of broken supersymmetry. S

Scientific paper

10.1103/PhysRevD.51.4503

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.

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