Abstract
We perform a systematic search for globally defined MSSM-like and left–right symmetric models on D6-branes on the T6/(Z2×Z6×ΩR) orientifold with discrete torsion. Our search is exhaustive for models that are independent of the value of the one free complex structure modulus. Preliminary investigations suggest that there exists one prototype of visible sector for MSSM-like and another for left–right symmetric models with differences arising from various hidden sector completions to global models. For each prototype, we provide the full matter spectrum, as well as the Yukawa and other three-point couplings needed to render vector-like matter states massive. This provides us with tentative explanations for the mass hierarchies within the quark and lepton sectors. We also observe that the MSSM-like models correspond to explicit realisations of the supersymmetric DFSZ axion model, and that the left–right symmetric models allow for global completions with either completely decoupled hidden sectors or with some messenger states charged under both visible and hidden gauge groups.
Highlights
String theory is arguably the most promising framework for a unified description of all fundamental interactions
This Z3 symmetry pops up when we mod out the centres of the overall non-Abelian gauge group from the discrete symmetries found as solutions to the necessary and sufficient conditions (55) and (57), i.e. we find that the quotient group (Z2 × Z33 × Z6)/(Z33 × Z22) is homomorphic to a Z3 symmetry with charge assignments listed in Table 25, after reduction of Z6 → Z3
The emphasis in this article lies on systematic scans for MSSM-like and left–right symmetric models on the considered toroidal orbifold background, which form consistent Type IIA/ R string vacua where the gauge degrees of freedom are attributed to D6-branes wrapping fractional, ideally rigid, three-cycles stuck at Z2 × Z2 orbifold singularities
Summary
String theory is arguably the most promising framework for a unified description of all fundamental interactions. On the T 6/(Z4 × R) [15] and T 6/(Z2 × Z4 × R) [16,17,18,19] backgrounds, it is impossible to construct globally defined supersymmetric D6-brane models with three quark generations, while on T 6/(Z6 × R) [20,18,21, 22] and T 6/(Z6 × R) [23,24,25,26,27,22] such models have been obtained For the latter, diverse investigations of the related low-energy effective field theory were performed in [22,28,29,30,31], discrete remnants of gauge symmetries were first investigated in [32], and the relation to some Peccei– Quinn symmetry and axions was studied in [33,34]. To prepare the systematic search and classification of global MSSM-like and left–right symmetric models in Sections 4 and 5, the second part of this section reviews some results about the search for appropriate local rigid D6-brane configurations allowing for three chiral quark generations with a minimal amount of undesired exotic matter, as first presented in [36]
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