N = 1 supersymmetric SU(4) × SU(2)L × SU (2)R effective theory from the weakly coupled heterotic superstring

Abstract In the context of the free-fermionic formulation of the heterotic superstring, we construct a three-generation N = 1 supersymmetric SU(4) × SU(2)L × SU(2)R model supplemented by an SU(8) hidden gauge symmetry and five Abelian factors. The symmetry breaking to the standard model is achieved using vacuum expectation values of a Higgs pair in ( 4,2 R ) + ( 4 ,2 R ) at a high scale. One linear combination of the Abelian symmetries is anomalous and is broken by vacuum expectation values of singlet fields along the flat directions of the superpotential. All consistent string vacua of the model are completely classified by solving the corresponding system of F- and D-flatness equations including non-renormalizable terms up to sixth order. The requirement of existence of electroweak massless doublets imposes further restrictions to the phenomenologically viable vacua. The third generation fermions receive masses from the tree-level superpotential. Further, a complete calculation of all non-renormalizable fermion mass terms up to fifth order shows that in certain string vacua the hierarchy of the fermion families is naturally obtained in the model as the second and third generation fermions earn their mass from fourth- and fifth-order terms. Along certain flat directions it is shown that the ratio of the SU(4) breaking scale and the reduced Planck mass is equal to the up quark ratio m c m t at the string scale. An additional prediction of the model, is the existence of a U(1) symmetry carried by the fields of the hidden sector, ensuring thus the stability of the lightest hidden state. It is proposed that the hidden states may account for the invisible matter of the universe.