Possibility of Spontaneous Symmetry Breaking in the Nambu-Jona-Lasinio model with torsion

We discuss the Nambu-Jona-Lasinio (NJL) model in curved space-time with torsion in the leading order of the $1\mathrm{/}N$ expansion. The effective potential of the torsion sector is calculated using the new technique based on the nonlocal part of anomaly-induced action which was recently found to produce the effective potential in the low-energy limit. The spontaneous symmetry breaking caused by the change of the torsion term is found, confirming the statements known from the existing literature. Furthermore, the gap equation is calculated as a function of curvature and torsion. Finally, the behavior of the effective four fermions coupling constant as a function of the torsion is discussed.