GROSS-NEVEU MODEL ON A SPHERE WITH A MAGNETIC MONOPOLE

We study, for the first time, the phase structure of the Gross-Neveu m odel with a combination of a (constant) gravitational and a magnetic f ield. This has been made possible by our finding of an exact solution to the problem, namely, the effective potential for the composite ferm ions. Then, from the corresponding implicit equation, the phase diagra m for the dynamical fermion mass is calculated numerically for some va lues of the magnetic field. For a small magnetic field the phase diagr am hints at the possibility of a second order phase transition at some critical curvature. With a growing magnetic field only the phase with broken chiral symmetry survives, because the magnetic field prevents the decay of the chiral condensate, This results is bound to have impo rtant consequences in early Universe cosmology.