We construct a three family flipped SU(5) model from the heterotic string theory compactified on the Z 12−I orbifold with one Wilson line. The gauge group is SU(5)This model does not derive any nonabelian group except SU(5) from E 8 , which is possible only for two cases in case of one shift V , one in Z 12−I and the other in Z 12−II . We present all possible Yukawa couplings. We place the third quark family in the twisted sectors and two light quark families in the untwisted sector. From the Yukawa couplings, the model provides the R-parity, the doublet-triplet splitting, and one pair of Higgs doublets. It is also shown that quark and lepton mixings are possible. So far we have not encountered a serious phenomenological problem. There exist vectorlike flavor SU (5)
The vanishing cosmological constant in the four-dimensional space-time is obtained in a 5D Randall-Sundrum model with a brane (B1) located at y = 0. The matter fields can be located at the brane. For settling any vacuum energy generated at the brane to zero, we need a three-index antisymmetric tensor field A(MNP) with a specific form for the Lagrangian. For the self-tuning mechanism, the bulk cosmological constant should be negative.
We construct a supersymmetric standard model in the context of the Z 12−I orbifold compactification of the heterotic string theory. The gauge group is SU(3) c × SU(2) L × U(1) Y × U(1) 4 × [SO(10) × U(1) 3 ] ′ . We obtain three chiral families, 3 × {Q, d c , u c , L, e c , ν c }, and Higgs doublets. There are numerous neutral singlets many of which can have VEVs so that low energy phenomenology on Yukawa couplings can be satisfied. In one assignment (Model E) of the electroweak hypercharge, we obtain the string scale value of sin 2 θ 0 W = 3 8 and another exactly massless exphoton (in addition to the photon) coupling to exotic particles only. There are color triplet and anti-triplet exotics, α and α, SU(2) L doublet exotics, δ and δ, and SU (3) We show that all these vector-like exotics achieve heavy masses by appropriate VEVs of neutral singlets. One can find an effective R-parity between light (electroweak scale) particles so that proton and the LSP can live sufficiently long. In another assignment (Model S) of the electroweak hypercharge, there does not appear any exotic particle but sin 2 θ 0 W = 3 14 .In E 8 ×E ′ 8 heterotic orbifold compactification, a model is completely determined with (1) a twist vector φ, which is associated with the compactified 3 dimensional complex (or 6 dimensional real) space, (2) a shift vector V which is associated with the 16 dimensional "gauge coordinate" and (3) Wilson line introduced in the compactified space. We employ the Z 12−I orbifold specified with the twist vector φ = ( 5 12 4 12 1 12 ), and take the following (b) H-momentum conservation with φ = 5 12 , 4 12 , 1 12 , z R 1 (z) = −1 mod 12, z R 2 (z) = 1 mod 3, z R 3 (z) = 1 mod 12, (2.17)where z(≡ A, B, C, . . . ) denotes the index of states participating in a vertex operator.
In family unification models, all three families of quarks and leptons are grouped together into an irreducible representation of a simple gauge group, thus unifying the standard model gauge symmetries and a gauged family symmetry. Large orthogonal groups, and the exceptional groups E 7 and E 8 , have been much studied for family unification. The main theoretical difficulty of family unification is the existence of mirror families at the weak scale. It is shown here that family unification without mirror families can be realized in simple fivedimensional and six-dimensional orbifold models similar to those recently proposed for SU(5) and SO(10) grand unification. It is noted that a family unification group that survived to near the weak scale and whose coupling extrapolated to high scales unified with those of the standard model would be evidence, accessible in principle at low energy, of the existence of small ͑Planckian or GUT-scale͒ extra dimensions.
We discuss a brane based inflationary scenario in which an initially non-supersymmetric configuration involving a D4 brane is dynamically transformed into a supersymmteric one in a background space-time geometry determined by a stack of D6 branes. Inflation is realized in the effective four dimensional theory and ends after reaching a stable BPS configuration. The scalar spectral index turns out to be 0.98. Under some simplifying assumption the reheat temperature, Hubble constant and the string scale are estimated to be of order 10 8 GeV, 10 12 GeV and 10 16 GeV, respectively.
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