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Motivated by the data from Super-Kamiokande and elsewhere indicating oscillations of atmospheric and solar neutrinos, we study charged-lepton-flavour violation, in particular the radiative decays µ → eγ and τ → µγ, but also commenting on µ → 3e and τ → 3µ/e decays, as well as µ → e conversion on nuclei. We first show how the renormalization group may be used to calculate flavour-violating soft supersymmetrybreaking masses for charged sleptons and sneutrinos in models with universal input parameters. Subsequently, we classify possible patterns of lepton-flavour violation in the context of phenomenological neutrino mass textures that accommodate the SuperKamiokande data, giving examples based on Abelian flavour symmetries. Then we calculate in these examples rates for µ → eγ and τ → µγ, which may be close to the present experimental upper limits, and show how they may distinguish between the different generic mixing patterns. The rates are promisingly large when the soft supersymmetry-breaking mass parameters are chosen to be consistent with the cosmological relic-density constraints. In addition, we discuss µ → e conversion on Titanium, which may also be accessible to future experiments.

We propose a new mechanism of (geometric) moduli stabilisation in type IIB/F-theory four-dimensional compactifications on Calabi-Yau manifolds, in the presence of 7-branes, that does not rely on non-perturbative effects. Complex structure moduli and the axion-dilaton system are stabilised in the standard way, without breaking supersymmetry, using 3-form internal fluxes. Kähler class moduli stabilisation utilises perturbative string loop corrections, together with internal magnetic fields along the D7-branes world-volume leading to Fayet-Iliopoulos D-terms in the effective supergravity action. The main ingredient that makes the stabilisation possible at a de Sitter vacuum is the logarithmic dependence of the string loop corrections in the large two-dimensional transverse volume limit of the 7-branes.

Motivated by recent work on low energy unification, in this short note we derive corrections on Newton's inverse square law due to the existence of extra decompactified dimensions. In the four-dimensional macroscopic limit we find that the corrections are of Yukawa type. Inside the compactified space of n-extra dimensions the sub-leading term is proportional to the (n + 1)-power of the distance over the compactification radius ratio. Some physical implications of these modifications are briefly discussed.