$Z_3$ orbifold construction of $SU(3)^3$ GUT with $\sin^2\theta_W^0=3/8$

Abstract

It is argued that a phenomenologically viable grand unification model from superstring is $SU(3)^3$, the simplest gauge group among the grand unifications of the electroweak hypercharge embedded in semi-simple groups. We construct a realistic 4D $SU(3)^3$ model with the GUT scale $\sin^2\theta_W^0= \frac38$ in a $Z_3$ orbifold with Wilson line(s). By two GUT scale vacuum expectation values, we obtain a rank 4 supersymmetric standard model below the GUT scale, and predict three more strange families.