Doublet-triplet splitting in fertile left-right symmetric heterotic string vacua

Abstract

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)

Novel Perspectives in String Phenomenology

“…Systematic classification of fermionic Z 2 × Z 2 heterotic-string orbifolds has been pursued since 2003. The classification of vacua with unbroken SO(10) gauge group was performed in [28] and extended to vacua with: SO(6) × SO(4) subgroup in [29]; SU (5) × U (1) subgroup in [30]; [32,33]. In the free fermionic classification method the string models are produced by a fixed set of boundary condition basis vectors, consisting of between twelve to fourteen basis vectors,…”

“…Number of exophobic models versus number of generations in SU (5) × U (1) string models. The free fermionic random classification methodology reaches its utility limit in the classification of SLM [31] and LRS models [32,33]. In both cases the models contain two vectors that break the SO(10) GUT symmetry.…”

“…In this manner a space of 10 7 three generation Standard-like Models with the standard light and heavy Higgs states was produced [31]. Tables 1 and 2 present a comparison of the methods in the case of the LRS models [32,33]. It is evident from the two tables that the fertile core method [33] facilitates the extraction of phenomenologically viable models when the total space of models becomes exceedingly large.…”

“…Tables 1 and 2 present a comparison of the methods in the case of the LRS models [32,33]. It is evident from the two tables that the fertile core method [33] facilitates the extraction of phenomenologically viable models when the total space of models becomes exceedingly large. On the other hand, it allows the analysis of general properties of the space of vacua, which is not the case in the genetic algorithm…”

“…Alon E Faraggi method [35]. The stage is now ripe for the application of novel computational methods for the identification of the fertility conditions [36].…”