A String Model with $SU(4)\times O(4)\times [Sp(4)]_{Hidden}$ Gauge Symmetry

In the four dimensional free fermionic formulation of the heterotic string, a semi-realistic $SU(4)\times SU(2)_L \times SU(2)_R$ model is proposed with three fermion generations in $(4,2,1)+(\bar 4,1,2)$ representations. The gauge symmetry of the model breaks to the standard gauge group using a higgs pair in the $(4,1,2)+(\bar 4,1,2)$ representations. The massless spectrum includes exotic fractionally charged states with non -- trivial transformation properties under part ($Sp(4)$) of the non -- abelian `hidden' symmetry. Finally there is a mirror pair in $(4,2,1) , (\bar 4,2,1)$ allowing the possibility for an identical running of $g_{4,L,R}$ couplings between the string and $SU(4)$ breaking scales. This is of crucial importance for a successful prediction of the weak mixing angle. Potential shortcomings and problems of the construction are analysed and possible solutions are discussed.