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Register a new userTetrahedral Symmetry A$_{bf 4}$ in Anti-SU(5) GUT
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We construct a flavor model in an anti-SU(5) GUT with a tetrahedral symmetry $A_4$. We choose a basis where $Q_{text{em}}=-frac13$ quarks and charged leptons are already mass eigenstates. This choice is possible from the $A_4$ symmetry. Then, matter representation $overline{10}_{-1}^{rm, matter}$ contains both a quark doublet and a heavy neutrino $N$, which enables us to use the $A_4$ symmetry to both $Q_{text{em}}=+frac23$ quark masses and neutrino masses (through the see-saw via $N$). This is made possible because the anti-SU(5) breaking is achieved by the Higgs fields transforming as anti-symmetric representations of SU(5), $overline{10}_{-1}^Hoplus 10_{+1}^H$, reducing the rank-5 anti-SU(5) group down to the rank-4 standard model group smg. For possible mass matrices, the $A_4$ symmetry predictions on mass matrices at field theory level are derived. Finally, an illustration from string compactification is presented.
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In string compactifications, frequently there appears the anomalous U(1) gauge symmetry which belonged to E8$times$E8 of the heterotic string. This anomalous U(1) gauge boson obtains mass at the compactification scale, just below $10^{18,}$GeV, by absorbing one pseudoscalar (corresponding to the model-independent axion) from the second rank anti-symmetric tensor field $B_{MN}$. Below the compactification scale, there results a global symmetry U(1)$_{rm anom}$ whose charge $Q_{rm anom}$ is the original gauge U(1) charge. This is the most natural global symmetry, realizing the invisible axion. This global symmetry U(1)$_{rm anom}$ is suitable for a flavor symmetry. In the simplest compactification model with the flipped SU(5) grand unification, we calculate all the low energy parameters in terms of the vacuum expectation values of the standard model singlets.
We study the feasibility of realizing supersymmetric new inflation model, introduced by Senoguz and Shafi in [1], for $SU(5)$ and flipped $SU(5)$ models of grand unified theories (GUTs). This realization requires an additional $U(1)_R times Z_{n}$ symmetry for its successful implementation. The standard model (SM) gauge singlet scalar components of $24_H$ and $10_H$ GUT Higgs superfields are respectively employed to realize successful inflation in $SU(5)$ and flipped $SU(5)$ models. The predictions of the various inflationary observables lie within the recent Planck bounds on the scalar spectral index, $n_s$, for $n geq 5$ in $SU(5)$ model and for $n geq 6$ in flipped $SU(5)$ model. In particular, the tensor to scalar ratio $r$ and the running of spectral index $d n_s/ dln k$ are negligibly small and lie in the range, $10^{-12} lesssim r lesssim 10^{-8}$ and $10^{-9} lesssim dn_s/dln k lesssim 10^{-3}$, for realistic values of $n$. In numerical estimation of the various predictions, we fix the gauge symmetry breaking scale, $M$, around $2 times 10^{16}$ GeV. The issue of gauge coupling unification in $R$-symmetric $SU(5)$ is evaded by adding vectorlike families with mass splitting within their multiplets. The dilution of monopoles beyond the observable limit is naturally achieved in the breaking of $SU(5)$ gauge symmetry during inflation. A realistic scenario of reheating with non-thermal leptogenesis is employed for both models. The predicted range of reheat temperature within Planck bounds, $3 times 10^{7}text{ GeV }lesssim T_r lesssim 2 times 10^{9}$ GeV, is safe from the gravitino problem for the gravitino mass, $m_{3/2} gtrsim 10$ TeV. Finally, the $U(1)_R times Z_{n}$ symmetry is also observed to play a crucial role in suppressing the various fast proton decay operators.
We minimally extend the Standard Model field content by adding new vector-like fermions at the TeV scale to allow gauge coupling unification at a realistic scale. We embed the model into a $SU(5)$ grand unified theory that is asymptotically safe and features an interacting fixed point for the gauge coupling. There are no Landau poles of the $U(1)$ gauge and Higgs couplings. Gauge, Yukawa and Higgs couplings are retraced from the fixed point and matched at the grand unification scale to those of the Standard Model rescaled up to the same energy. All couplings, their fixed point values and critical exponents always remain in the perturbative regime.
We explore the gauge coupling relations and the unification scale in F-theory SU(5) GUT broken down to the Standard Model by an internal U(1)Y gauge flux. We consider variants with exotic matter representations which may appear in these constructions and investigate their role in the effective field theory model. We make a detailed investigation on the conditions imposed on the extraneous matter to raise the unification scale and make the color triplets heavy in order to avoid fast proton decay. We also discuss in brief the implications on the gaugino masses.
We discuss the $SU(5)$ grand unified extension of flavour models with multiple modular symmetries. The proposed model involves two modular $S_4$ groups, one acting in the charged fermion sector, associated with a modulus field value $tau_T$ with residual $Z_3^T$ symmetry, and one acting in the right-handed neutrino sector, associated with another modulus field value $tau_{SU}$ with residual $Z_2^{SU}$ symmetry. Quark and lepton mass hierarchies are naturally generated with the help of weightons, which are SM singlet fields, where their non-zero modular weights play the role of Froggatt-Nielsen charges. The model predicts TM$_1$ lepton mixing, and neutrinoless double beta decay at rates close to the sensitivity of current and future experiments, for both normal and inverted orderings, with suppressed corrections from charged lepton mixing due to the triangular form of its Yukawa matrix.
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