Preference for a Vanishingly Small Cosmological Constant in Supersymmetric Vacua in a Type IIB String Theory Model

We study the probability distribution P(\Lambda) of the cosmological constant \Lambda in a specific set of KKLT type models of supersymmetric IIB vacua. We show that, as we sweep through the quantized flux values in this flux compactification, P(\Lambda) behaves divergent at \Lambda =0^- and the median magnitude of \Lambda drops exponentially as the number of complex structure moduli h^{2,1} increases. Also, owing to the hierarchical and approximate no-scale structure, the probability of having a positive Hessian (mass squared matrix) approaches unity as h^{2,1} increases.Comment: 6 pages, 2 figures; v2: version to appear in PL

Three-Family SU(5) Grand Unification in String Theory

We present two 3-family SU(5) grand unified models in the heterotic string theory. One model has 3 chiral families and 9 pairs of $5+{\overline 5}$ Higgs fields, and an asymptotically-free SU(2) X SU(2) hidden sector, where the two SU(2)s have different matter contents. The other model has 6 left-handed and 3 right-handed 10s, 12 left-handed and 9 right-handed ${\overline 5}$s, and an asymptotically-free SU(3) hidden sector. At the string scale, the gauge couplings $g^2$ of the hidden sector are three times as big as that of SU(5). In addition, both models have an anomalous U(1).Comment: 11 pages, Revtex 3.0, minor misprints correcte