CHIRAL-SYMMETRY BREAKING IN THE NAMBU-JONA-LASINIO MODEL IN CURVED SPACETIME WITH A NONTRIVIAL TOPOLOGY

We discuss the phase structure (in the 1/N expansion) of the Nambu-Jon a-Lasinio model in curved spacetime with nontrivial topology M3 X S1. The evaluation of the effective potential of the composite field psips iBAR is presented in the linear curvature approximation (topology is t reated exactly) and in the leading order of the 1/N expansion. The com bined influence of topology and curvature to the phase transitions is investigated. It is shown, in particular, that at zero curvature and f or small radius of the torus there is a second order phase transition from the chiral symmetric to the chiral nonsymmetric phase. When the c urvature grows and (or) the radius of S1 decreases, then the phase tra nsition is in general of first order. The dynamical fermionic mass is also calculated in a number of different situations.