We examine the stabilization of the two typical moduli, the length ρ of the eleventh segment and the volume V of the internal six manifold, in compactified heterotic M -theory. It is shown that, under certain conditions, the phenomenologically favored vacuum expectation values of ρ and V can be obtained by the combined effects of multi-gaugino condensations on the hidden wall and the membrane instantons wrapping the three cycle of the internal six manifold.
It is suggested that various hierarchy problems in supersymmetric standard model, i.e. the Yukawa hierarchies, the µ problem, and the suppression of dangerous baryon and/or lepton number (B/L) violating couplings, are resolved altogether in the framework of horizontal U(1) symmetry whose spontaneous breaking results in the appearance of one expansion parameter (the Cabibbo angle). Within a reasonable range of U(1) charges, there exist a few models compatible with experiments. The specific sizes of B/L violating couplings of these models are calculated and several phenomenological consequences are discussed.
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