PHASE-STRUCTURE OF RENORMALIZABLE 4-FERMION MODELS IN SPACETIMES OF CONSTANT CURVATURE

A number of 2D and 3D four-fermion models which are renormalizable, in the 1/N expansion, in a maximally symmetric constant curvature space are investigated. To this purpose, a powerful method for the exact stu dy of spinor heat kernels and propagators on maximally symmetric space s is reviewed. The renormalized effective potential is found for any v alue of the curvature and its asymptotic expansion is given explicitly , both for small and for strong curvature. The influence of gravity on the dynamical symmetry-breaking pattern of some U(2) flavorlike and d iscrete symmetries is described in detail. The phase diagram in S-2 is constructed and it is shown that, for any value of the coupling const ant, a curvature exists above which chiral symmetry is restored. For t he case of H-2, chiral symmetry is always broken. In three dimensions, in the case of positive curvature, S-3, it is seen that curvature can induce a second-order phase transition. For H-3 the configuration giv en by the auxiliary fields equated to zero is not a solution of the ga p equation. The physical relevance of the results is discussed.