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Register a new userOrbifold SUSY GUT from the Heterotic String
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Authors
Bumseok Kyae
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From the string partition function, we discuss the mass-shell and GSO projection conditions valid for Kaluza-Klein (KK) as well as massless states in the heterotic string theory compactified on a nonprime orbifold. Based on the obtained conditions we construct a 4D string standard model, which is embedded in a 6D SUSY GUT by including KK states above the compactification scale. We discuss the stringy threshold corrections to gauge couplings, including the Wilson line effects.
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Using Z3 asymmetric orbifolds in heterotic string theory, we construct N=1 SUSY three-generation models with the standard model gauge group SU(3)_C times SU(2)_L times U(1)_Y and the left-right symmetric group SU(3)_C times SU(2)_L times SU(2)_R times U(1)_{B-L}. One of the models possesses a gauge flavor symmetry for the Z3 twisted matter.
We study a class of Little String Theories (LSTs) of A type, described by $N$ parallel M5-branes spread out on a circle and which in the low energy regime engineer supersymmetric gauge theories with $U(N)$ gauge group. The BPS states in this setting correspond to M2-branes stretched between the M5-branes. Generalising an observation made in arXiv:1706.04425, we provide evidence that the BPS counting functions of special subsectors of the latter exhibit a Hecke structure in the Nekrasov-Shatashvili (NS) limit, i.e. the different orders in an instanton expansion of the supersymmetric gauge theory are related through the action of Hecke operators. We extract $N$ distinct such reduced BPS counting functions from the full free energy of the LST with the help of contour integrals with respect to the gauge parameters of the $U(N)$ gauge group. Physically, the states captured by these functions correspond to configurations where the same number of M2-branes is stretched between some of these neighbouring M5-branes, while the remaining M5-branes are collapsed on top of each other and a particular singular contribution is extracted. The Hecke structures suggest that these BPS states form the spectra of symmetric orbifold CFTs. We furthermore show that to leading instanton order (in the NS-limit) the reduced BPS counting functions factorise into simpler building blocks. These building blocks are the expansion coefficients of the free energy for $N=1$ and the expansion of a particular function, which governs the counting of BPS states of a single M5-brane with single M2-branes ending on it on either side. To higher orders in the instanton expansion, we observe new elements appearing in this decomposition, whose coefficients are related through a holomorphic anomaly equation.
We show that Supersymmetric models with Type I seesaw neutrino masses support slow roll inflection point inflation. The inflaton is the D-flat direction labelled by the chiral invariant HLN composed of the Higgs(H), slepton(L) and conjugate sneutrino(N) superfields. The scale of inflation and fine tuning is set by the conjugate neutrino Majorana mass $M_{ u^c} sim 10^6-10^{12}$ GeV. The cubic term in the (quartic) inflaton potential is dominantly from superpotential (not soft Susy breaking) couplings. The tuning conditions are thus insensitive to soft supersymmetry breaking parameters and are generically much less stringent than for previous `A-term inflation scenarios controlled by mass scales $sim TeV$. WMAP limits on the ratio of tensor to scalar perturbations limit the scale $M$ controlling inflection point inflation: $M <7.9 times 10^{13}$ GeV. `Instant preheating is operative and dumps the inflaton energy into MSSM modes giving a high reheat temperature : $T_{rh} approx M_{ u^c}^{3/4}, 10^{6}$ GeV $sim 10^{11}- 10^{15} $ GeV. A large gravitino mass $> 50 $ TeV is therefore required to avoid over closure by reheat produced gravitinos. `Instant preheating and NLH inflaton facilitate production of right handed neutrinos during inflaton decay and thus non-thermal leptogenesis in addition to thermal leptogenesis. We show that the embedding in the fully realistic New Minimal Supersymmetric SO(10) GUT requires use of the heaviest righthanded neutrino mass as the controlling scale but the possibility of a measurable tensor scalar perturbation ratio seems marginal. We examine the parametric difficulties remaining.
We build explicit supersymmetric unification models where grand unified gauge symmetry breaking and supersymmetry (SUSY) breaking are caused by the same sector. Besides, the SM-charged particles are also predicted by the symmetry breaking sector, and they give the soft SUSY breaking terms through the so-called gauge mediation. We investigate the mass spectrums in an explicit model with SU(5) and additional gauge groups, and discuss its phenomenological aspects. Especially, nonzero A-term and B-term are generated at one-loop level according to the mediation via the vector superfields, so that the electro-weak symmetry breaking and 125 GeV Higgs mass may be achieved by the large B-term and A-term even if the stop mass is around 1 TeV.
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.
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