A generic class of string theories predicts the existence of light moduli fields, and they are expected to have masses m φ comparable to the gravitino mass m 3/2 which is in a range of 10 −2 keV-1GeV in gauge-mediated supersymmetry breaking theories. Such light fields with weak interactions suppressed by the Planck scale can not avoid some stringent cosmological constraints, that is, they suffer from 'cosmological moduli problems'. We show that all the gravitino mass region 10 −2 keV < ∼ m 3/2 < ∼ 1GeV is excluded by the constraints even if we incorporate a late-time mini-inflation (thermal inflation). However, a modification of the original thermal inflation model enables the region 10 −2 keV < ∼ m 3/2 < ∼ 500keV to survive the constraints. It is also stressed that the moduli can be dark matter in our universe for the mass region 10 −2 keV < ∼ m φ < ∼ 100keV.

The dilaton field in string theories (if exists) is expected to have a mass of the order of the gravitino mass m 3/2 which is in a range of 10 −2 keV-1GeV in gauge-mediated supersymmetry breaking models. If it is the case, the cosmic energy density of coherent dilaton oscillation easily exceeds the critical density of the present universe. We show that even if this problem is solved by a late-time entropy production (thermal inflation) a stringent constraint on the energy density of the dilaton oscillation is derived from experimental upperbounds on the cosmic X(γ)-ray backgrounds. This excludes an interesting mass region, 500keV < ∼ m 3/2 < ∼ 1GeV, in gauge-mediated supersymmetry breaking models.

We examine the X-ray spectrum from the decay of the dark-matter moduli with mass ∼ O(100)keV, in particular, paying attention to the line spectrum from the moduli trapped in the halo of our galaxy. It is found that with the energy resolution of the current experiments (∼ 10%) the line intensity is about twice stronger than that of the continuum spectrum from the moduli that spread in the whole universe. Therefore, in the future experiments with higher energy resolutions it may be possible to detect such line photons. We also investigate the γ-ray spectrum emitted from the decay of the multi-GeV moduli. It is shown that the emitted photons may form MeV-bump in the γ-ray spectrum. We also find that if the modulus mass is of the order of 10 GeV, the emitted photons at the peak of the continuum spectrum loses their energy by the scattering and the shape of the spectrum is significantly changed, which makes the constraint weaker than that obtained in the previous works.

We show that the brane configuration describing the Izawa-Yanagida-IntriligatorThomas (IYIT) model with gauged U (1) subgroup of the global symmetry contains inconsistent geometry, implying that there exists a stable vacuum where supersymmetry is dynamically broken.

We find the Seiberg-Witten geometry for four dimensional N = 2 supersymmetric E 6 gauge theories with massless fundamental hypermultiplets, by geometrically embedding them in type II string theories compactified on Calabi-Yau threefolds. The resulting geometry completely agrees with that of recent works, which are based on the technique of N = 1 confining phase superpotentials. We also derive the Seiberg-Witten geometry for E 7 gauge theories with massive fundamental hypermultiplets.