We study 10D super Yang-Mills theory with the gauge groups E 6 , E 7 and E 8 . We consider the torus/orbifold compacfitication with magnetic fluxes and Wilson lines. They lead to 4D interesting models with three families of quarks and leptons, whose profiles in extra dimensions are quasi-localized because of magnetic fluxes.1 See for a review [25] and references therein.

We study 10D super Yang-Mills E 8 theory on the 6D torus compactification with magnetic fluxes. We study systematically the possibilities for realizing 4D supersymmetric standard models with three generations of quarks and leptons. We also study quark mass matrices.

We present an inflationary scenario based on a phenomenologically viable model with direct gauge mediation of low-scale supersymmetry breaking. Inflation can occur in the supersymmetry-breaking hidden sector. Although the reheating temperature from the inflaton decay is so high that the gravitino problem seems to be severe, late time entropy production from the decay of the pseudomoduli field associated with the supersymmetry breaking can dilute gravitinos sufficiently. We show that gravitinos are also produced from the pseudomoduli decay and there is a model parameter space where gravitinos can be the dark matter in the present universe. * Cosmological inflation [1,2] in the early universe is now considered as a part of the "standard" cosmology. It can solve many cosmological problems such as the horizon problem and the flatness problem. It also accounts for the origin of the primordial fluctuations [3]. In most models of inflation, a scalar field with the flat potential (called the inflaton) which drives inflation is assumed to be outside the standard model of particle physics since there is almost no inflaton candidate in this framework. 1 Then, a natural question is how inflation dynamics is embedded in a particle physics model beyond the standard model. To construct an inflation model, it is reasonable to respect supersymmetry (SUSY), which is one of the most promising candidates for physics beyond the standard model, because the radiative corrections for scalar fields are suppressed in supersymmetric theories and an inflaton potential can be naturally flattened.If SUSY is realized in nature, it must be broken at some energy scale. We usually leave its dynamics to a SUSY breaking hidden sector and the SUSY breaking effect is transmitted to the visible sector by some interactions. Gauge mediation is an attractive mechanism, which uses the standard model gauge interactions [7,8] (For recent general arguments, see Ref.[9]). It naturally suppresses the unwanted flavor-changing processes due to flavor blindness of the gauge interactions. While many gauge mediation models are already known, the model proposed by Kitano, Ooguri and Ookouchi (KOO) [10] is a distinguished one (see also Ref. [11]). This model is based on the recent development of metastable SUSY breaking in supersymmetric QCD (SQCD) started from the work of Intriligator, Seiberg and Shih (ISS)[12] and is classified as so-called direct gauge mediation models [13] where the flavor symmetries of a hidden SUSY breaking sector are weakly gauged and identified with the standard model gauge symmetries. The KOO model can generate sizable gaugino masses while many direct gauge mediation models suffer from anomalously small gaugino masses [14] (see also Ref. [15]). However, since the vacuum considered in the KOO model (the ISS vacuum) is not the global minimum of the potential, it is necessary to impose several conditions on the model parameters in order to guarantee the vacuum stability. In particular, two hierarchical mass scales are required in the flavors o...

We study anomaly mediation models with gauge mediation effects from messengers which have a general renormalizable mass matrix with a supersymmetry-breaking spurion. Our models lead to a rich structure of supersymmetry breaking terms in the visible sector. We derive sum rules among the soft scalar masses for each generation. Our sum rules for the first and second generations are the same as those in general gauge mediation, but the sum rule for the third generation is different because of the top Yukawa coupling. We find the parameter space where the tachyonic slepton problem is solved. We also explore the case in which gauge mediation causes the anomalously small gaugino masses. Since anomaly mediation effects on the gaugino masses exist, we can obtain viable mass spectrum of the visible sector fields. *

We propose a simple high-scale inflationary scenario based on a phenomenologically viable model with direct gauge mediation of low-scale supersymmetry breaking. Hybrid inflation is occurred in a hidden supersymmetry breaking sector. Two hierarchical mass scales to reconcile both high-scale inflation and gauge mediation are necessary for the stability of the metastable supersymmetry breaking vacuum. Our scenario is also natural in light of the Landau pole problem of direct gauge mediation.Comment: 10 pages; v2: presentation changed, qualitative results unchanged, references added; v3: minor correction, published in PT