Heterotic road to the MSSM withRparity

Abstract

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.

Proton hexality in local grand unification

“…One canonical choice is SO (12). For this discussion it is more convenient to use Cartan-Weyl notation.…”

“…Here, all 60 roots are generated by permuting underlined entries, resulting in the 60 + 6 = 66 dimensional adjoint of SO (12). Apart from the adjoint, the following SO(12) representations, specified by their weights, will be of interest for us 32:…”

“…String theory could be a candidate as it also includes a consistent description of gravitational interactions. 1 Recent work towards string theoretic constructions of the minimal supersymmetric standard model (MSSM) [8][9][10][11][12] has revealed the concept of "Local Grand Unification" [8,13,14], a variant of GUTs that addresses some of its problematic properties. It allows "split multiplets" that e.g.…”

Three-generation asymmetric orbifold models from heterotic string theory

“…Now we can easily read off momentum modes with orbifold phase p · V ∼ 1/3 as 12) and no solution for p (5) . These states survive the orbifold projection when combined with the right-moving H-momentum states (2.7), resulting in the following chiral supermultiplets: table 2 for U(1) charges).…”

“…Especially, in the framework of heterotic Z N or Z N × Z M orbifold compactifications [1,2], embedding a supersymmetric standard model or a higher dimensional grand unified theory into heterotic string theory is considered [3][4][5][6][7][8][9][10][11][12][13][14] (also see a review [15]). Since strings on an orbifold can be described by a solvable worldsheet conformal field theory [16,17], it is possible to calculate Yukawa couplings and selection rules [18][19][20][21][22].…”