Superstring standard model from Bbb Z_12−Iorbifold compactification with and without exotics, and effectiveR-parity

Abstract

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.

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