We consider the $L$-$R$ symmetric composite model for quarks and leptons where constituent preons possessing some local $SU(N)_{MF}$ metaflavor symmetry are bound by the chiral $SO(n)_{L}\times SO(n)_{R}$ gauge metacolor forces. The strengthening of the 't Hooft's anomaly matching condition, when the massless fermion composites are required to complete a single representation of the $SU(N)_{MF}$ rather than some set of its representations, allows to fix the number of basic metaflavors $N$. Particularly, just eight left-handed and eight right-handed preons and their composites preserving the global chiral symmetry $SU(8)_{L}\times SU(8)_{R}$ are turned out to underlie the physical world at small distances that uniquely identifies the local metaflavor symmetry $SU(8)_{MF}$ as its effective unified symmetry. We next show that the spontaneous $L$-$R$ symmetry violation caused by composite scalars reduces this initially vectorlike $SU(8)_{MF}$ theory down to the conventional $SU(5)$ GUT with an extra local family symmetry $SU(3)_{F}$ and three standard families of quarks and leptons. Though the tiny confinement scale for universal preons composing both quarks and leptons makes it impossible to directly confirm their composite nature, simultaneous emergence of several extra $SU(5)\times SU(3)_{F}$ multiplets of heavy composite fermions may help with a model verification. Generally, they may be located at scales from $O(100)$ $TeV$ up to the Planck mass scale depending on an interplay between the compositeness scale and scale of the family symmetry $SU(3)_{F}$. Some of them through a natural see-saw mechanism provide neutrino masses which, in contrast to conventional picture, appear to follow an inverted family hierarchy. Others mix with ordinary quark-lepton families in a way that there may arise a marked violation of unitarity in the CKM matrix for leptons.
We discuss renormalization group equations for gauge coupling constants in gauge-Higgs grand unification on five-dimensional Randall-Sundrum warped space. We show that all the four-dimensional Standard Model gauge coupling constants are asymptotically free and are effectively unified in $SO(11)$ gauge-Higgs grand unified theories on 5D Randall-Sundrum warped space.
The effective Higgs theories at the TeV scale in supersymmetric $SU(5)$ grand unification models are systematically derived. Restricted to extensions on $\mathbf{5}_{H}$ containing the Higgs sector we show that only two types of real (vector-like) models and one type of chiral model are found to be consistent with perturbative grand unification. While the chiral model has been excluded by the LHC data, the fate of perturbative unification will be uniquely determined by the two classes of vector-like models.
We apply the perturbative grand unification due to renormalization to distinguish TeV-scale relics of supersymmetric $\rm{SO}(10)$ scenarios. With rational theoretical constraints taken into account, we find that for the breaking pattern of either $\rm{SU}(5)$ or Pati-Salam only extra matter $\mathbf{16}$ supermultiplet of $SO(10)$ can appear at TeV scale, apart from MSSM spectrum.
SU(5) $\otimes$ SU(5) provides a minimal grand unification scheme for fermions and gauge forces if there are vector-like quarks and leptons in nature. We explore the gauge coupling unification in a non-supersymmetric model of this type, and study its implications for proton decay. The properties of vector-like quarks and intermediate scales that emerge from coupling unification play a central role in suppressing proton decay. We find that in this model, the familiar decay mode $p \to e^+ π^0$ may have a partial lifetime within the reach of currently planned experiments.
Supersymmetric grand unification based on $SO(10)$ is one of the most attractive paradigms in physics beyond the Standard Model. Inspired by the recent NANOGrav signal, we discuss the implications of detecting a stochastic gravitational wave background emitted by a network of cosmic strings for the $SO(10)$ grand unification. Starting from a minimal model with multiple steps of symmetry breaking, we show that it generally prefers a high intermediate scale above $10^{14}\, \mathrm{GeV}$ that is favored by observable primordial gravitational waves. The observed spectrum can potentially narrow th…
We explicitly test the asymptotic grand unification of a minimal 5-dimensional model with SO(10) gauge theory compactified on an $S^{1}/Z_{2}\times Z^{\prime}_{2}$ orbifold. We consider all matter fields as propagating in the bulk and show that the gauge couplings asymptotically run to a fixed point in the UV. However, the Yukawa couplings will typically hit a Landau pole right above the compactification scale in this class of SO(10) models.
4D Higgs field is identified with the extra-dimensional component of gauge potentials in the gauge-Higgs unification scenario. $SO(5) \times U(1)$ gauge-Higgs EW unification in the Randall-Sundrum warped space is successful at low energies. The Higgs field appears as an Aharonov-Bohm phase $θ_H$ in the fifth dimension. Its mass is generated at the quantum level and is finite. The model yields almost the same phenomenology as the standard model for $θ_H < 0.1$, and predicts $Z'$ bosons around 6 - 10 TeV with very broad widths. The scenario is genelarized to $SO(11)$ gauge-Higgs grand unificatio…
