GROSS-NEVEU MODEL AND THE SUPERSYMMETRIC AND NONSUPERSYMMETRIC NAMBU-JONA-LASINIO MODEL IN A MAGNETIC-FIELD

The infrared dynamics in the (3+1)-dimensional supersymmetric and nons upersymmetric Nambu-Jona-Lasinio model in a constant magnetic field is studied. While at strong coupling the dynamics in these two models is essentially different, it is shown that the models become equivalent at weak coupling. In particular, at weak coupling, as the strength of the magnetic field goes to infinity, both the supersymmetric and nonsu persymmetric Nambu-Jona-Lasinio models are reduced to a continuum set of independent (1+1)-dimensional Gross-Neveu models, labeled by the co ordinates in the plane perpendicular to the magnetic field. The releva nce of these results for cosmological models based on supersymmetric d ynamics is pointed out.