We explore a "fertile patch" of the heterotic landscape based on a 6 -II orbifold with SO(10) and E 6 local GUT structures. We search for models allowing for the exact MSSM spectrum. Our result is that of order 100 out of a total 3 × 10 4 inequivalent models satisfy this requirement.

In a previous paper, referred to as a "Mini-Landscape" search, we explored a "fertile patch" of the heterotic landscape based on a 6 -II orbifold with SO(10) and E 6 local GUT structures. In the present paper we extend this analysis. We find many models with the minimal supersymmetric standard model spectra and an exact R parity. In all of these models, the vector-like exotics decouple along D flat directions. We present two "benchmark" models which satisfy many of the constraints of a realistic supersymmetric model, including non-trivial Yukawa matrices for 3 families of quarks and leptons and Majorana neutrino masses for right-handed neutrinos with non-trivial See-Saw masses for the 3 light neutrinos. In an appendix we comment on the important issue of string selection rules and in particular the so-called "gammarule".• In ML [40], at the last step in our analysis of a theory, we evaluated the effective mass operators, for the vector-like exotics, up to order 8 in fields. If all the exotics obtained mass, the model was retained. When calculating the rank of the mass matrices, we assumed that requiring the singlet configuration to respect supersymmetry would not change the result.1 Note, a handful of heterotic string models with MSSM-like structure have been discussed in the literature [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39].2 Note even if one relaxes this constraint as a prior it was shown that 90% of the MSSM-like models satisfying sin 2 θW = 3/8 at the string scale necessarily satisfy this constraint [62]. Also, the discrepancy between the string scale, O(10 17 GeV), and the 4D GUT scale, O(10 16 GeV), can in principle be resolved by threshold corrections due to states near the string scale.

Orbifold compactification of heterotic E 8 × E ′ 8 string theory is a source for promising grand unified model building. It can accommodate the successful aspects of grand unification while avoiding problems like doublet-triplet splitting in the Higgs sector. Many of the phenomenological properties of the 4-dimensional effective theory find an explanation through the geometry of compact space and the location of matter and Higgs fields. These geometrical properties can be used as a guideline for realistic model building.

Abstract:The recent detection of the cosmic microwave background polarimeter experiment BICEP2 of tensor fluctuations in the B-mode power spectrum basically excludes all plausible axion models where its decay constant is above 10 13 GeV. Moreover, there are strong theoretical, astrophysical, and cosmological motivations for models involving, in addition to the axion, also axion-like particles (ALPs), with decay constants in the intermediate scale range, between 10 9 GeV and 10 13 GeV. Here, we present a general analysis of models with an axion and further ALPs and derive bounds on the relative size of the axion and ALP photon (and electron) coupling. We discuss what we can learn from measurements of the axion and ALP photon couplings about the fundamental parameters of the underlying ultraviolet completion of the theory. For the latter we consider extensions of the Standard Model in which the axion and the ALP(s) appear as pseudo Nambu-Goldstone bosons from the breaking of global chiral U(1) (Peccei-Quinn (PQ)) symmetries, occurring accidentally as low energy remnants from exact discrete symmetries. In such models, the axion and the further ALP are protected from disastrous explicit symmetry breaking effects due to Planck-scale suppressed operators. The scenarios considered exploit heavy right handed neutrinos getting their mass via PQ symmetry breaking and thus explain the small mass of the active neutrinos via a seesaw relation between the electroweak and an intermediate PQ symmetry breaking scale. For a number of explicit models, we determine the parameters of the low-energy effective field theory describing the axion, the ALPs, and JHEP06 (2014)037 their interactions with photons and electrons, in terms of the input parameters, in particular the PQ symmetry breaking scales. We show that these models can accommodate simultaneously an axion dark matter candidate, an ALP explaining the anomalous transparency of the universe for γ-rays, and an ALP explaining the recently reported 3.55 keV gamma line from galaxies and clusters of galaxies, if the respective decay constants are of intermediate scale. Moreover, they do not suffer severely from the domain wall problem.