Realistic four-generation MSSM in Type II string theory

We construct a four-generation MSSM with rank-4 Yukawa matrices from intersecting D6 branes on a T⁶/(Z₂×Z₂)$T^6/({\mathbb{Z}}_2\times {\mathbb{Z}}_2)$ orientifold. The Yukawa matrices obtained provide an example of Flavor Democracy (FD), where the Yukawa couplings are all nearly equal. Mass hierarchies may then be generated by slight perturbations away from FD. We find that it is possible to obtain hierarchical masses for the quarks and leptons of each generation and mixings between them. In addition, the tree-level gauge couplings are unified at the string scale. Finally, we also construct similar models with one, two, and three generations in which the rank of the Yukawa matrices is equal to the number of generations in each model.