Discrete Abelian gauge symmetries and axions

We combine two popular extensions of beyond the Standard Model physics within the framework of intersecting D6-brane models: discrete n symmetries and Peccei-Quinn axions. The underlying natural connection between both extensions is formed by the presence of massive U(1) gauge symmetries in D-brane model building. Global intersecting D6-brane models on toroidal orbifolds of the type T6/Z2N and T6/Z2 × Z2M with discrete torsion offer excellent playgrounds for realizing these extensions. A generation-dependent Z2 symmetry is identified in a global Pati-Salam model, while global left-right symmetric models give rise to supersymmetric realizations of the DFSZ axion model. In one class of the latter models, the axion as well as Standard Model particles carry a non-trivial Z3 chargeThis work is partially supported by the Cluster of Excellence PRISMA DGF no. EXC 1098 and the DFG research grant HO 4166/2-1. W.S. is supported by the ERC Advanced Grant SPLE under contract ERC-2012-ADG-20120216-320421, by the grant FPA2012-32828 from the MINECO, and the grant SEV-2012-0249 of the \Centro de Excelencia Severo Ochoa" Programm