Model building on the non-factorisable type IIA ${\mathbf{T}}^{\mathbf{6}}\mathbf{/}({\mathbb{Z}}_{\mathbf{4}}\times \mathbf{\Omega }\mathcal{R})$ orientifold

We construct global semi-realistic supersymmetric models with intersecting D6-branes on the non-factorisable orientifold $T^6\mathrm{/}({\mathbb{Z}}_4\times \mathrm{\Omega }\mathcal{R})$. The non-factorisable structure gives rise to differences compared to the factorisable case: additional conditions for the three-cycles to be Lagrangian and extra constraints on the wrapping numbers for building fractional cycles.