We study the cosmology of supersymmetric models in which the supersymmetry breaking effects are mediated by gauge interactions at about the 10 5 GeV scale. We first point out that the gravitino is likely to overclose the Universe in this class of models. This requires an entropy production, which prefers a baryogenesis mechanism at a relatively low temperature. The Affleck-Dine mechanism for baryogenesis is one of the possibilities to generate enough baryon asymmetry, but the analysis is non-trivial since the shape of the potential for the flat direction differs substantially from the conventional hidden sector case. To see this, we first perform a 2-loop calculation to determine the shape of the potential. By combining the potential with the supergravity contribution, we then find that the Affleck-Dine baryogenesis works efficiently to generate sufficient baryon asymmetry. On the other hand, we also point out that string moduli fields, if present, are stable and their coherent oscillations overclose the Universe by more than 15 orders of magnitude. One needs a very late inflationary period with an e-folding of N > ∼ 5 and an energy density of < ∼ (10 7 GeV) 4 . A thermal inflation is enough for this purpose. Fortunately, the Affleck-Dine baryogenesis is so efficient that enough baryon asymmetry can survive the late inflation. * This work was supported in part by the

Seiberg duality in supersymmetric gauge theories is the claim that two different theories describe the same physics in the infrared limit. However, one cannot easily work out physical quantities in strongly coupled theories and hence it has been difficult to compare the physics of the electric and magnetic theories. In order to gain more insight into the equivalence of two theories, we study the ''e ϩ e Ϫ '' cross sections into ''hadrons'' for both theories in the superconformal window. We describe a technique which allows us to compute the cross sections exactly in the infrared limit. They are indeed equal in the low-energy limit and the equality is guaranteed because of the anomaly matching condition. The ultraviolet behavior of the total ''e ϩ e Ϫ '' cross section is different for the two theories. We comment on proposed non-supersymmetric dualities. We also analyze the agreement of the ''␥␥'' and ''WW'' scattering amplitudes in both theories, and in particular try to understand if their equivalence can be explained by the anomaly matching condition.

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We study the Next-to-Minimal Supersymmetric Standard Model (NMSSM) as the simplest candidate solution to the µ-problem in the context of the gauge mediation of supersymmetry breaking (GMSB). We first review various proposals to solve the µ-problem in models with the GMSB. We find none of them entirely satisfactory and point out that many of the scenarios still lack quantitative studies, and motivate the NMSSM as the simplest possible solution. We then study the situation in the Minimal Supersymmetric Standard Model (MSSM) with the GMSB and find that an order 10% cancellation is necessary between the µ-parameter and the soft SUSY-breaking parameters to correctly reproduce M Z . Unfortunately, the NMSSM does not to give a phenomenologically viable solution to the µ-problem. We present quantitative arguments which apply both for the low-energy and high-energy GMSB and prove that the NMSSM does not work for either case. Possible modifications to the NMSSM are then discussed. The NMSSM with additional vector-like quarks works phenomenologically, but requires an order a few percent cancellation among parameters. We point out that this cancellation has the same origin as the cancellation required in the MSSM.

Supersymmetry with R-parity violation ͑RPV͒ provides an interesting framework for naturally accommodating small neutrino masses. Within this framework, we discuss the lepton-flavor violating ͑LFV͒ processes →e␥, →eee, and →e conversion in nuclei. We make a detailed study of the observables related to LFV in different RPV models, and compare them to the expectations of R-conserving supersymmetry with heavy right-handed neutrinos. We show that the predictions are vastly different and uniquely characterize each model, thus providing a powerful framework for experimentally distinguishing between different theories of LFV. In addition to the obvious possibility of amplified tree-level generation of →eee and →e conversion in nuclei, we find that even in the case where these processes arise at the one-loop level, their rates are comparable to that of →e␥, in clear contrast to the predictions of R-conserving models. We conclude that, in order to distinguish between the different models, such a combined study of all the LFV processes is necessary, and that measuring P-odd asymmetries in polarized →eee can play a decisive role. We also comment on the intriguing possibility of RPV models yielding a large T-odd asymmetry in the decay of polarized →eee.

We address the issue of lepton flavor violation and neutrino masses in the ''fat-brane'' paradigm, where flavor changing processes are suppressed by localizing different fermion field wave functions at different positions ͑in the extra dimensions͒ in a thick brane. We study the consequences of suppressing lepton number violating charged lepton decays within this scenario for lepton masses and mixing angles. In particular, we find that charged lepton mass matrices are constrained to be quasidiagonal. We further consider whether the same paradigm can be used to naturally explain small Dirac neutrino masses by considering the existence of three right-handed neutrinos in the brane, and discuss the requirements to obtain phenomenologically viable neutrino masses and mixing angles. Finally, we examine models where neutrinos obtain a small Majorana mass by breaking lepton number in a far away brane and show that, if the fat-brane paradigm is the solution to the absence of lepton number violating charged lepton decays, such models predict, in the absence of flavor symmetries, that charged lepton flavor violation will be observed in the next round of rare muon or tau decay experiments.

We discuss CP violation in the quark sector within a novel approach to the Yukawa puzzle proposed by Arkani-Hamed and Schmaltz, where Yukawa hierarchies result from localising the Standard Model quark field wave-functions, at different positions (in the extra dimensions) in a "fat-brane." We show that at least two extra dimensions are necessary in order to obtain sufficient CP violation, while reproducing the correct quark mass spectrum and mixing angles. * gbranco@thwgs.cern.ch and gbranco@cfif.ist.utl.pt †