The Gross-Neveu Model and the Supersymmetric and Non–Supersymmetric Nambu–Jona–Lasinio Model in a Magnetic Field

The infrared dynamics in the (3 + 1)–dimensional supersymmetric and non–supersymmetric 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 non–supersymmetric Nambu–Jona–Lasinio models are reduced to a continuum set of independent (1+1)–dimensional Gross–Neveu models, labeled by the coordinates in the plane perpendicular to the magnetic field. The relevance of these results for cosmological models based on supersymmetric dynamics is pointed out.