The Aligned SU(5) times U(1)² Model

In Calabi-Yau string compactification, it is pointed out that there exists a new type of $SU(5) \times U(1)^2$ model (the aligned $SU(5) \times U(1)^2$ model) in which the $SU(5)$ differs from the standard $SU(5)$ and also from the flipped $SU(5)$. With the aid of the discrete symmetry suggested from Gepner model, we construct a simple and phenomenologically interesting three-generation model with the aligned $SU(5) \times U(1)^2$ gauge symmetry. The triplet-doublet splitting problem can be solved. It is also found that there is a realistic solution for solar neutrino problem and for the $\mu $-problem. At low energies this model is in accord with the minimal supersymmetric standard model except for the existence of singlet fields with masses of $O(1)$TeV.