Reduction of N=1, E8 SYM over SU(3)/U(1)×U(1)×Z3 and its four-dimensional effective action

We propose an extension of the Standard Model inspired by the E8×E8 Heterotic String. In order that a reasonable effective Lagrangian is presented we neglect everything else other than the ten-dimensional N=1 supersymmetric Yang-Mills sector associated with one of the gauge factors and certain couplings necessary for anomaly cancellation. We consider a compactified space-time M4×B0/Z3, where B0 is the nearly Kähler manifold SU(3)/U(1)×U(1) and Z3 is a freely acting discrete group on B0. Then we reduce dimensionally the E8 on this manifold and we employ the Wilson flux mechanism leading in four dimensions to an SU(3)3 gauge theory with the spectrum of a N=1 supersymmetric theory. We compute the effective four-dimensional Lagrangian and demonstrate that an extension of the Standard Model is obtained with interesting features including a conserved baryon number and fixed tree level Yukawa couplings and scalar potential. The spectrum contains new states such as right-handed neutrinos and heavy vector-like quarks.