The classification method of the free fermionic heterotic string vacua is extended to models where the SO(10) GUT symmetry is broken directly at the string scale to the Left-Right Symmetric subgroup. Our method involves using a fixed set of basis vectors which are defined by the boundary conditions assigned to the free fermions before enumerating the string vacua by varying the Generalised GSO (GGSO) projection coefficients. It allows the derivation of algebraic expressions for the GGSO projections for each sector that generates massless states in the models. This enables a computerised analysis of the entire massless spectrum of a given choice of GGSO projection coefficients. The total number of vacua in the class of models chosen is 2 66 ≈ 7.38 × 10 19 . A statistical sampling is performed and a sample size of 10 11 vacua with the Left-Right Symmetric gauge group is extracted. We present the results of the classification, noting that contrary to the previous classification of Pati-Salam models, no three generation exophobic models were found. The results obtained demonstrate the existence of three generation models with the necessary Higgs representations needed for viable spontaneous symmetry breaking, and with a leading top quark Yukawa

Classification of Left-Right Symmetric (LRS) heterotic-string vacua in the free fermionic formulation, using random generation of Generalised GSO (GGSO) projection coefficients, produced phenomenologically viable models with probability 4×10 −11 . Extracting substantial number of phenomenologically viable models requires modification of the classification method. This is achieved by identifying phenomenologically amenable conditions on the Generalised GSO projection coefficients that are randomly generated at the SO(10) level. Around each of these fertile cores we perform a complete LRS classification, generating viable models with probabilility 1.4 × 10 −2 , hence increasing the probability of generating phenomenologically viable models by nine orders of magnitude, and producing some 1.4 × 10 5 such models. In the process we identify a doublet-triplet selection mechanism that operates in twisted sectors of the string models that break the SO(10) symmetry to the Pati-Salam subgroup. This mechanism therefore operates as well in free fermionic models with Pati-Salam and Standard-like Model SO (10)

Systematic classification of Z 2 × Z 2 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.

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