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.

We study possible correlations between properties of the observable and hidden sectors in heterotic string theory. Specifically, we analyze the case of the Z 6 -II orbifold compactification which produces a significant number of models with the spectrum of the supersymmetric standard model. We find that requiring realistic features does affect the hidden sector such that hidden sector gauge group factors SU(4) and SO(8) are favored. In the context of gaugino condensation, this implies low energy supersymmetry breaking. DOI: 10.1103/PhysRevLett.98.181602 PACS numbers: 11.25.Wx, 04.65.+e, 12.60.Cn, 12.60.Jv In the string theory landscape [1][2][3][4][5], the minimal supersymmetric standard model (MSSM) corresponds to a certain subset of vacua out of a huge variety. To obtain string theory predictions, one can first identify vacua with realistic properties, and then analyze their common features. In this Letter, we study possible implications of this approach for supersymmetry breaking. First, we look for models consistent with the MSSM at low energies, then we study common features of their hidden sectors which are responsible for supersymmetry breaking.We find that requiring realistic features affects the hidden sector such that, in the context of gaugino condensation, low energy supersymmetry breaking is favored. Since high energy supersymmetry is usually required by consistency of string models, this correlation provides a top-down motivation for low energy supersymmetry, which is favored by phenomenological considerations such as the gauge hierarchy problem and electroweak symmetry breaking.We base our study [6] on the orbifold compactifications [7,8] of the E 8 E 8 heterotic string [9]. Recent work on an orbifold GUT interpretation of heterotic models [10 -12] has facilitated construction of realistic models. In particular, the Z 6 -II orbifold (see [12]) has been shown to produce many models with realistic features [6,13,14]. These include the gauge group and the matter content of the MSSM, gauge coupling unification and a heavy top quark. Such models are generated using the gauge shifts These shifts are chosen due to their ''local grand unified theory (GUT)'' [13][14][15][16] properties. They lead to massless matter in the first twisted sector (T 1 ) forming a 16-plet of SO (10) the hypercharge will be that of standard 4D GUTs. These features facilitate construction of realistic models.We focus on models with one Wilson line of order 3 (W 3 ) and one Wilson line of order 2 (W 2 ), although we include all models with 2 Wilson lines in the statistics. These are the simplest constructions allowing for 3 MSSM matter families without chiral exotics. In this case, two matter generations have similar properties while the third family is different. Selection of realistic models proceeds as follows: (1) Steps (1)-(7) are described in detail in Ref. [6]. At the last step, we select models in which the decoupling of the SM exotic states is possible without breaking the largest gauge group in the hidden sector. ...

We review recent progress in embedding the supersymmetric standard model into string theory. We discuss how, with the incorporation of certain aspects of grand unification, a search strategy can be developed that allows to efficiently find rather large numbers of promising string vacua. Global string-derived models with the following features are discussed: (i) exact MSSM spectrum below the unification scale; (ii) R parity; (iii) hierarchical Yukawa couplings with nontrivial mixing; (iv) solution to the µ problem; (v) see-saw suppressed neutrino masses.a

Models with modular flavor symmetries have been thought to be highly predictive. We point out that these predictions are subject to corrections from non-holomorphic terms in the Lagrangean. Specifically, in the models discussed in the literature, the Kähler potential is not fixed by the symmetries, for instance. The most general Kähler potential consistent with the symmetries of the model contains additional terms with additional parameters, which reduce the predictive power of these constructions. We also comment on how one may conceivably retain the predictivity. arXiv:1909.06910v1 [hep-ph]