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Register a new userPartly Supersymmetric Grand Unification
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Authors
Tony Gherghetta
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It is shown how grand unification can occur in models which are partly supersymmetric. The particle states which are composite do not contribute to the running of gauge couplings above the compositeness scale, while the elementary states contribute the usual large logarithmns. This introduces a new differential running contribution to the gauge couplings from partly composite SU(5) matter multiplets. In particular, for partly supersymmetric models, the incomplete SU(5) elementary matter multiplets restore gauge coupling unification even though the usual elementary gaugino and Higgsino contributions need not be present.
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Gauge-Higgs grand unification is formulated. By extending $SO(5) times U(1)_X$ gauge-Higgs electroweak unification, strong interactions are incorporated in $SO(11)$ gauge-Higgs unification in the Randall-Sundrum warped space. Quarks and leptons are contained in spinor and vector multiplets of $SO(11)$. Although the KK scale can be as low as $10 $ TeV, proton decay is forbidden by a conserved fermion number in the absence of Majorana masses of neutrinos.
We discuss a grand unified theory (GUT) based on a $USp(32)$ GUT gauge group broken to its subgroups including a special subgroup. A GUT based on an $SO(32)$ GUT gauge group has been discussed on six-dimensional (6D) orbifold space $M^4times T^2/mathbb{Z}_2$. It is inspired by the $SO(32)$ string theory behind the $SU(16)$ GUT whose $SU(16)$ is broken to a special subgroup $SO(10)$. Alternative direction is to embed an $SU(16)$ gauge group into a $USp(32)$ GUT gauge group, which is inspired by a non-supersymmetric symplectic-type $USp(32)$ string theory. In a $USp(32)$ GUT, one generation of the SM fermions is embedded into a 6D bulk Weyl fermion in a $USp(32)$ defining representation. For a three generation model, all the 6D and 4D gauge anomalies in the bulk and on the fixed points are canceled out without exotic chiral fermions at low energies. The SM Higgs scalar is embedded into a 6D bulk scalar field in a $USp(32)$ adjoint representation.
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 the possible range of the cosmic string scale and restricts the unified couplings and the unification scale by requiring gauge coupling unification. As an indirect consequence of the high cosmic string scale, the monopole abundance places non-trivial constraints on the theory. These are complementary to the proton decay constraints and probe different facets of supersymmetric $SO(10)$ unification theories.
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.
$SO(11)$ gauge-Higgs grand unification is formulated in the six-dimensional hybrid warped space in which the fifth and sixth dimensions play as the electroweak and grand-unification dimensions. Fermions are introduced in ${bf 32}$, ${bf 11}$ and ${bf 1}$ of $SO(11)$. Small neutrino masses naturally emerge as a result of a new seesaw mechanism in the gauge-Higgs unification which is characterized by a $3 times 3$ mass matrix.
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