Classification of left–right symmetric heterotic string vacua

Abstract

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

Spinor-Vector Duality and BSM Phenomenology

“…This led to the discovery of Spinor-Vector Duality (SVD) in the space of fermionic Z 2 × Z 2 orbifold compactification, where the duality transformation is induced by exchange of GGSO phases. The classification method was subsequently extended to vacua with: SO(6) × SO(4) [36]; SU(5) × U(1) [37]; [39,40], unbroken subgroups of SO (10). In this classification method the string models are generated by a fixed set of boundary condition basis vectors, consisting of twelve to fourteen basis vectors, B = {v 1 , v 2 , .…”

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.…”

On Non-Supersymmetric String Model Building

“…For the purposes of our analysis we will consider a class of heterotic string models in the Free Fermionic Formulation (FFF) [23,24]. This framework is convenient for the study of the spectra as we can utilise the classification formalism developed in [25,26,27,29,30,31,32]. We will focus on a semi-realistic set of models with gauge symmetry SO(10) × SO(8) 2 × U(1) 9 , where the SO (10) factor is assumed to be the "observable" gauge group.…”