Towards machine learning in the classification of Z 2 × Z 2 orbifold compactifications

Systematic classification of Z2 × Z2 orbifold compactifications of the heterotic-string was pursued by using its free fermion formulation. The method entails random generation of string vacua and analysis of their entire spectra, and led to discovery of spinor-vector duality and three generation exophobic string vacua. The classification was performed for string vacua with unbroken SO(10) GUT symmetry, and progressively extended to models in which the SO(10) symmetry is broken to the SO(6) × SO(4), SU(5) × U(1), SU(3) × SU(2) × U(1)2 and SU(3) × U(1) × SU(2)2 subgroups. Obtaining sizeable numbers of phenomenologically viable vacua in the last two cases requires identification of fertility conditions. Adaptation of machine learning tools to identify the fertility conditions will be useful when the frequency of viable models becomes exceedingly small in the total space of vacua.