Spinor–vector duality in heterotic SUSY vacua

Niemeier Lattices in the Free Fermionic Heterotic–String Formulation

“…The role of the basis vectors 2 and 3 in the models of (15) and (18) is to generate the twisted realisation of the gauge symmetry enhancement of the (8) gauge groups arising from the null sector. We may further represent the spinor-vector duality in an orbifold representation [42] and translate the duality map in (19) to distinct choices of the toroidal background fields [24,43]. Generalisation of the spectral map transformation between heterotic-string vacua was extended to Gepner models in [44].…”

Non-tachyonic semi-realistic non-supersymmetric heterotic-string vacua

“…The basis vectors underlying the NAHE-based models therefore differ by the additional three or four basis vectors that extend the NAHE set. The second route follows from the classification methodology that was developed in [52] for the classification of type II free fermionic superstrings and adopted in [18][19][20][21]23,[46][47][48] for the classification of free fermionic heterotic-string vacua with SO(10) GUT symmetry and its Pati-Salam [20,21] and flipped SU (5) [23] subgroups. The main difference between the two classes of models is that while the NAHE-based models allow for asymmetric boundary conditions with respect to the set of internal fermions {y, ω|ȳ,ω}, the classification method only utilises symmetric boundary conditions.…”

“…This distinction affects the moduli spaces of the models [53], which can be entirely fixed in the former case [54] but not in the later. On the other hand the classification method enables the systematic scan of spaces of the order of 10 12 vacua, and led to the discovery of spinor-vector duality [46][47][48][55][56][57][58][59] and exophobic heterotic-string vacua [20,21]. In this paper, for reasons that will be clarified below, our discussion is focussed on the NAHE-based models.…”

“…For completeness we discuss the construction of such models by using the classification methods of [18][19][20][21]23,[46][47][48]. In this approach the set of basis vectors is fixed and a large number of string models, of the order of 10 12 vacua, is spanned by enumerating the independent GGSO projection coefficients.…”

“…One can then resort to a complete [46][47][48] or statistical sampling 1 of the total space [18,19], and classify the models by their twisted matter spectrum. The classification is facilitated by expressing the GGSO projections in algebraic form [18,19,[46][47][48]. The analysis of the entire spectrum of the string models is computerised and vacua with specific phenomenological characteristics can be fished our from the larger space of models.…”