Classification of three generation superstring models according to their discrete symmetries

Abstract

Compactification of the ten dimensional heterotic E 8 × E′ 8 string theory on a Calabi-Yau (C-Y) manifold leads to discrete symmetries which play a crucial role in phenomenological and cosmological applications. In view of this, we classify all possible models with distinct groups of discrete symmetries which emerge from the only known three generation C-Y manifold constructed by Tian and Yau. We find forty five groups of discrete symmetries together with the corresponding complex structures of this manifold. Each of these groups is a subgroup of at least one of three basic groups of discrete symmetries. We also derive the transformation properties of the lepton, quark and antiquark fields of the theory under these basic groups in the case where the gauge group after flux breaking is SU(3) c × SU(3) L × SU(3) R. The transformation properties of the fields under any other group of discrete symmetries can then be readily deduced.