Split NMSSM from dimensional reduction of a $10D$, $\mathcal{N}=1$, $E_8$ theory over a modified flag manifold

We review the Standard Model extension that results from the dimensional reduction of a $10D$, $\mathcal{N}=1$, $E_8$ gauge theory over the $M_4 \times SU(3)/U(1) \times U(1) \times \mathbf{Z}_3$ space, which leads to a $4D$, $\mathcal{N}=1$, $SU(3)^3\times U(1)^2$ theory. Below the unification scale we obtain a Split NMSSM effective theory. The third generation quark and light Higgs masses are within the experimental limits at 2-loop level and the neutralino LSP mass is predicted $<800$ GeV.