Topological Chiral Symmetry Breaking in Susy Njl in Curved Spacetime

The effective potential in the model introduced by Buchbinder-Inagaki-Odintsov (BIO) [1] which represents SUSY NJL model non-minimally coupled with the external gravitational field is found. The topology of the space is considered to be non-trivial. Chiral symmetry breaking under the action of external curvature and non-trivial topology is investigated. Nambu-Jona-Lasinio (NJL) model represents one of the best solvable examples for the study of dynamical symmetry breaking. SUSY NJL has been introduced in ref. [2] and it does not contain examples of dynamical symmetry breaking. However, at the external fields such symmetry breaking is possible even in SUSY NJL as it has been shown recently in BIO version of the SUSY NJL model non-minimally coupled with external gravity [1] (for a review of four-fermion models at external fields, see [3]). In the applications of dynamical symmetry breaking to the early Universe it is important to take into account not only curvature, but also non-trivial