GUT with Anomalous U(1)A Suggests Heterotic M-Theory?

We show that a new GUT scenario we proposed indicates that heterotic M-theory is one of the most interesting possibility to describe our world because of the two features in the scenario. The first feature is that E6 unified group plays an essential role not only in understanding larger mixing angles in lepton sector than in quark sector but also in solving the SUSY flavor problem by introducing non-abelian horizontal symmetry SU(2)H or SU(3)H . The second feature is that the cutoff scale must be taken as the usual GUT scale ΛG ∼ 2× 10 16 GeV to realize natural gauge coupling unification. Because this cutoff scale is smaller than the Planck scale or string scale, it may suggest the existence of extra dimension in which only gravity modes can propagate. This talk is based on a dozen papars[1, 2, 3, 4, 5, 6, 7, 8, 9] some of which are collaborated with T. Yamashita, M. Bando and Q. Shafi. E-mail: [email protected] Table 1: Quantum numbers under E6×SU(2)H ×U(1)A×Z2 are presented only for all non-singlet fields under E6×SU(2)H except an doublet field X(1, 2)x which is required for Witten anomaly cancellation. MATTER Ψ(27,2)4 , Ψ(27,1) + 3/2 HIGGS(SU(2)H) F (1,2) + −3/2, F̄ (1, 2̄) + −5/2 HIGGS A(78,1) −1, A (78,1)5 E6 → Φ(27,1) + −3, C ′(27,1)−6 SU(3)C × U(1)EM Φ̄ (27,1)5 , C̄(27,1) − 0