A string model with SU(4) × O(4) × [Sp(4)]hidden gauge symmetry

In the four dimensional free fermionic formulation of the heterotic string, a semi-realistic SU(4) × SU(2)L × SU(2)R model is proposed with three fermion generations in (4,2,1) + (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) + (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), (4,2,1) allowing the possibility for an identical running of g4,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.