Classification of flipped SU(5)SU(5) heterotic-string vacua

We extend the classification of free fermionic heterotic-string vacua to models in which the SO(10)SO(10) GUT symmetry is reduced at the string level to the flipped SU(5)SU(5) subgroup. In our classification method the set of boundary condition basis vectors is fixed and the enumeration of string vacua is obtained in terms of the Generalised GSO (GGSO) projection coefficients entering the one-loop partition function. We derive algebraic expressions for the GGSO projections for all the physical states appearing in the sectors generated by the set of basis vectors. This enables the programming of the entire spectrum analysis in a computer code. For that purpose we developed two independent codes, based on FORTRAN95 and JAVA, and all results presented are confirmed by the two independent routines. We perform a statistical sampling in the space of 244∼1013244∼1013 flipped SU(5)SU(5) vacua, and scan up to 1012 GGSO configurations. Contrary to the corresponding Pati–Salam classification results, we do not find exophobic flipped SU(5)SU(5) vacua with an odd number of generations. We study the structure of exotic states appearing in the three generation models, that additionally contain a viable Higgs spectrum, and demonstrate the existence of models in which all the exotic states are confined by a hidden sector non-Abelian gauge symmetry, as well as models that may admit the racetrack mechanism.