Exotica and discreteness in the classification of string spectra

I discuss the existence of discrete properties in the landscape of free fermionic heterotic-string vacua that were discovered via their classification by SO(10) GUT models and its subgroups such as the Pati-Salam, Flipped SU(5) and SU(4) × SU(2) × U(1) models. The classification is carried out by fixing a set of basis vectors and varying the GGSO projection coefficients entering the one-loop partition function. The analysis of the models is facilitated by deriving algebraic expressions for the GSO projections that enable a computerised analysis of the entire string spectrum and the scanning of large spaces of vacua. The analysis reveals discrete symmetries like the spinor-vector duality observed at the SO(10) level and the existence of exophobic Pati-Salam vacua. Contrary to the Pati-Salam case the classification shows that there are no exophobic Flipped SU(5) vacua with an odd number of generations. It is observed that the SU(4) × SU(2) × U(1) models are substantially more constrained. (paper)