Various lepton-flavor violating (LFV) processes in the supersymmetric standard model with right-handed neutrino supermultiplets are investigated in detail. It is shown that large LFV rates are obtained when tan β is large. In the case where the mixing matrix in the lepton sector has a similar structure as the KobayashiMaskawa matrix and the third-generation Yukawa coupling is as large as that of the top quark, the branching ratios can be as large as Br(µ → eγ) ≃ 10 −11 and Br(τ → µγ) ≃ 10 −7 , which are within the reach of future experiments. If we assume a large mixing angle solution to the atmospheric neutrino problem, rate for the process τ → µγ becomes larger. We also discuss the difference between our case and the case of the minimal SU (5) grand unified theory.

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Cosmological issues are examined when gravitino is the lightest superparticle (LSP) and R-parity is broken. Decays of the next lightest superparticles occur rapidly via R-parity violating interaction, and thus they do not upset the bigbang nucleosynthesis, unlike the R-parity conserving case. The gravitino LSP becomes unstable, but its lifetime is typically much longer than the age of the Universe. It turns out that observations of diffuse photon background coming from radiative decays of the gravitino do not severely constrain the gravitino abundance, and thus the gravitino weighing less than around 1 GeV can be dark matter of the Universe when bilinear R-parity violation generates a neutrino mass which accounts for the atmospheric neutrino anomaly. *

We discuss issues in an attempt to put the Standard Model (SM) in fivedimensional anti-de Sitter spacetime compactified on S 1 /Z 2 . The recentlyproposed approach to the gauge hierarchy problem by using this background geometry, with the SM confined on a boundary, is extended to a situation where (some of) the SM particles reside in the five dimensional bulk. In particular, we find a localization of zero modes of bulk fermions near the boundary with a negative tension. Unlike the compactification with the flat metric, these fermion zero modes couple to Kaluza-Klein (KK) excitations of the SM gauge bosons. Interestingly, only low-lying modes of such KK gauge bosons have non-negligible couplings. Current electroweak precision data give a constraint that the first KK mode be heavier than 9 TeV. We also argue that at least the Higgs field should be confined on the brane to utilize the Randall-Sundrum background as a solution to the gauge hierarchy.

We examine the lepton-flavor violation caused by a Yukawa coupling matrix y ν,ij for right-handed neutrinos in the supersymmetric standard model. We stress that decay rates for τ → µγ and µ → eγ may reach the range to be accessible to near future experiments if left-right mixing terms in the slepton mass matrix are substantially large.

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We investigate gaugino condensation in the framework of the strongly coupled heterotic E 8 × E 8 string (M-theory). Supersymmetry is broken in a hidden sector and gravitational interactions induce soft breaking parameters in the observable sector. The resulting soft masses are of order of the gravitino mass. The situation is similar to that in the weakly coupled E 8 × E 8 theory with one important difference: we avoid the problem of small gaugino masses which are now comparable to the gravitino mass.