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Register a new userSO(10)-like Superstring Standard Model with R-parity from the Heterotic String
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We construct a supersymmetric standard model in the context of the Z_{12-I} orbifold compactification of the E_8 x E_8 heterotic string theory. The gauge group is SU(3)_c x SU(2)_L x U(1)_Y x U(1)^4 x [SO(10) x U(1)^3] with sin^2theta_W = 3/8. We obtain three families of SO(10) spinor-like chiral matter states, and Higgs doublets. All other extra states are exactly vector-like under the standard model gauge symmetry. There are numerous standard model singlets, many of which get VEVs such that only the standard model gauge symmetry survives and desired Yukawa couplings can be generated at lower energies. In particular, all vector-like exotic states achieve superheavy masses and the R-parity can be preserved.
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Recently it was proposed that the ten dimensional tachyonic superstring vacua may serve as good starting points for the construction of viable phenomenological models. Such phenomenologically viable models enlarge the space of possible string solutions, and may offer novel insight into some of the outstanding problems in string phenomenology. In this paper we present a three generation standard--like model that may be regarded as a compactification of a ten dimensional tachyonic vacuum. We discuss the features of the model as compared to a similar model that may be regarded as compactification of the ten dimensional $SO(16)times SO(16)$ heterotic-string. We further argue that in the four dimensional model all the geometrical moduli are fixed perturbatively, whereas the dilaton may be fixed by hidden sector non--perturbative effects.
Grand unification groups (GUTs) are constructed from SO(32) heterotic string via $Z_{12-I}$ orbifold compactification. So far, most phenomenological studies from string compactification relied on $EE8$ heterotic string, and this invites the SO(32) heterotic string very useful for future phenomenological studies. Here, spontaneous symmetry breaking is achieved by Higgsing of the anti-symmetric tensor representations of SU($N$). The anti-SU($N$) presented in this paper is a completely different class from the flipped-SU($N$)s from the spinor representations of SO($2N$). Here, we realize chiral representations: $tsixoplus 5cdot ineb $ for a SU(9) GUT and $3{{ten}_Loplus {fiveb}_L}$ for a SU(5)$$ GUT. In particular, we confirm that the non-Abelian anomalies of SU(9) gauge group vanish and hence our compactification scheme achieves the key requirement. We also present the Yukawa couplings, in particular for the heaviest fermion, $t$, and lightest fermions, neutrinos. In the supersymmetric version, we present a scenario how supersymmetry can be broken dynamically via the confining gauge group SU(9). Three families in the visible sector are interpreted as the chiral spectra of SU(5)$$ GUT.
We search for realistic supersymmetric standard-like models from SO(32) heterotic string theory on factorizable tori with multiple magnetic fluxes. Three chiral ganerations of quarks and leptons are derived from the adjoint and vector representations of SO(12) gauge groups embedded in SO(32) adjoint representation. Massless spectra of our models also include Higgs fields, which have desired Yukawa couplings to quarks and leptons at the tree-level.
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 $SU(3)_ctimes SU(2)_Ltimes U(1)_Ytimes U(1)^4times[SO(10)times U(1)^3]$. We obtain three chiral families, $3times{Q,d^c,u^c,L,e^c, u^c}$, 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 $sin^2theta_W^0={3/8}$ and another exactly massless {it exphoton} (in addition to the photon) coupling to exotic particles only. There are color triplet and anti-triplet exotics, $alpha$ and $bar{alpha}$, $SU(2)_L$ doublet exotics, $delta$ and $bar{delta}$, and $SU(3)_ctimes SU(2)_L$ singlet but $Y={2/3},-{1/3},-{2/3},{1/3}$ exotics, $xi,eta,bar{xi}, bar{eta}$. 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 $sin^2theta_W^0={3/14}$.
The strategy for assigning $Z_{4R}$ parity in the string compactification is presented. For the visible sector, an anti-SU(5) (flipped-SU(5)) grand unification (GUT) model with three families is used to reduce the number of representations compared to the number in the minimal supersymmetric standard models (MSSMs). The SO(32) heterotic string is used to allow a large nonabelian gauge group SU($N$), $Nge 9$, for the hidden sector such that the number of extra U(1) factors is small. A discrete subgroup of the gauge U(1)s is defined as the $Z_{4R}$ parity. Spontaneous symmetry breaking of anti-SU(5) GUT is achieved by the vacuum expectation values of two index antisymmetric tensor Higgs fields ${bf 10}_{+1}$ and $overline{bf 10}_{-1}$ that led to our word `anti-SU(5). In the illustrated example, the multiplicity 3 in one twisted sector allows the permutation symmetry $S_3$ that leads us to select the third family members and one MSSM pair of the Higgs quintets.
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