The heterotic-string models in the free fermionic formulation gave rise to some of the most realistic-string models to date, which possess N = 1 spacetime supersymmetry. Lack of evidence for supersymmetry at the LHC instigated recent interest in non-supersymmetric heterotic-string vacua. We explore what may be learned in this context from the quasi-realistic free fermionic models. We show that constructions with a low number of families give rise to proliferation of a priori tachyon producing sectors, compared to the non-realistic examples, which typically may contain only one such sector. The reason being that in the realistic cases the internal six dimensional space is fragmented into smaller units. We present one example of a quasi-realistic, nonsupersymmetric, non-tachyonic, heterotic-string vacuum and compare the structure of its massless spectrum to the corresponding supersymmetric vacuum. While in some sectors supersymmetry is broken explicitly, i.e. the bosonic and fermionic sectors produce massless and massive states, other sectors, and in particular those leading to the chiral families, continue to exhibit Fermi-Bose degeneracy. In these sectors the massless spectrum, as compared to the supersymmetric cases, will only differ in some local or global U (1) charges. We discuss the conditions for obtaining n b = n f at the massless level in these models. Our example model contains an anomalous U (1) symmetry, which generates a tadpole diagram at one-loop order in string perturbation theory. We speculate that this tadpole diagram may cancel the corresponding diagram generated by the one-loop non-vanishing vacuum energy and that in this respect the supersymmetric and non-supersymmetric vacua should be regarded on an equal footing. Finally we discuss vacua that contain two supersymmetry generating sectors. a

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Free fermionic models and symmetric heterotic toroidal orbifolds both constitute exact backgrounds that can be used effectively for phenomenological explorations within string theory. Even though it is widely believed that for Z 2 × Z 2 orbifolds the two descriptions should be equivalent, a detailed dictionary between both formulations is still lacking. This paper aims to fill this gap: we give a detailed account of how the input data of both descriptions can be related to each other. In particular, we show that the generalized GSO phases of the free fermionic model correspond to generalized torsion phases used in orbifold model building. We illustrate our translation methods by providing free fermionic realizations for all Z 2 × Z 2 orbifold geometries in six dimensions.

The spinor-vector duality was discovered in free fermionic constructions of the heterotic string in four dimensions. It played a key role in the construction of heterotic-string models with an anomaly-free extra symmetry that may remain unbroken down to low energy scales. A generic signature of the low scale string derived model is via diphoton excess that may be within reach of the LHC. A fascinating possibility is that the spinor-vector duality symmetry is rooted in the structure of the heterotic-string compactifications to two dimensions. The two-dimensional heterotic-string theories are in turn related to the so-called moonshine symmetries that underlie the two-dimensional compactifications. In this paper, we embark on exploration of this connection by the free fermionic formulation to classify the symmetries of the two-dimensional heterotic-string theories. We use two complementary approaches in our classification. The first utilises a construction which is akin to the one used in the spinor-vector duality. Underlying this method is the triality property of (8) representations. In the second approach, we use the free fermionic tools to classify the twenty-four-dimensional Niemeier lattices.

The space of (2, 0) models is of particular interest among all heterotic-string models because it includes the models with the minimal SO(10) unification structure, which is well motivated by the Standard Model of particle physics data. The fermionic Z 2 × Z 2 heterotic-string models revealed the existence of a new symmetry in the space of string configurations under the exchange of spinors and vectors of the SO(10) GUT group, dubbed spinor-vector duality. In this paper we generalize this idea to arbitrary internal rational conformal field theories (RCFTs). We explain how the spectral flow operator normally acting within a general (2, 2) theory can be used as a map between (2, 0) models. We describe the details, give an example and propose more simple currents that can be used in a similar way.