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Register a new userGeometric unification theory of the grand unification and gravitational interactions and new physics
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This paper discovers geometric unification theory of the grand unification and gravitational interactions and their new physics according to the general fiber bundle theory, symmetry and so on. Consequently, the research of this paper is based on the exact scientific bases of mathematics and physics. The Lagrangians of the grand unification and gravitational interactions are unifiedly deduced from quantitative causal principle (QCP) and satisfy the gauge invariant principle of general gauge fields interacting with Fermion and/or boson fields. The geometry and physics meanings of gauge invariant property of different physical systems are revealed, and it is discovered that all the Lagrangians of the four fundamental physics interactions are composed of the invariant quantities in corresponding spacetime structures. The difficulties that fundamental physics interactions and Noether theorem are not able to be unifiedly given and investigated are overcome, the geometric unification theory and origins of the four fundamental physics interactions and Noether theorem are shown by QCP, their two-order general Euler-Lagrange Equations and corresponding Noether conservation currents are derived in general curved spacetime. This paper further deduces QCP from symmetric principle. Consequently, geometric unification theory of the grand unification and gravitation theories and Noether theorem based on symmetric principle and the new physics are given in this paper. This paper further gives the unification of QCP and symmetric principle. Thus, this paper opens a door to both study and give new developments of geometric unification theory of physics laws, and using the new geometric unification theory, a lot of research works about different branches of physics can be anew done and expressed simpler with different symmetric characters.
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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.
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 $theta_H$ 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 $theta_H < 0.1$, and predicts $Z$ bosons around 6 - 10 TeV with very broad widths. The scenario is genelarized to $SO(11)$ gauge-Higgs grand unification. Fermions are introduced in the spinor and vector representations of $SO(11)$. Proton decay is naturally forbidden.
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.
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.
Given the tremendous phenomenological success of the Standard Model (SM) framework, it becomes increasingly important to understand to what extent its specific structure dynamically emerges from unification principles. In this study, we present a novel supersymmetric (SUSY) Grand Unification model based upon gauge trinification $[mathrm{SU}(3)]^3$ symmetry and a local $mathrm{SU}(2)_{mathrm{F}} times mathrm{U}(1)_{mathrm{F}}$ family symmetry. This framework is inspired by $mathrm{E}_8 to mathrm{E}_6times mathrm{SU}(2)_{mathrm{F}} times mathrm{U}(1)_{mathrm{F}}$ orbifold reduction pattern, with subsequent $mathrm{E}_6to [mathrm{SU}(3)]^3$ symmetry breaking step. In this framework, higher-dimensional operators of $mathrm{E}_6$ induce the threshold corrections in the gauge and Yukawa interactions leading, in particular, to only two distinct Yukawa couplings in the fundamental sector of the resulting $[mathrm{SU}(3)]^3times mathrm{SU}(2)_{mathrm{F}} times mathrm{U}(1)_{mathrm{F}}$ Lagrangian. Among the appealing features emergent in this framework are the Higgs-matter unification and a unique minimal three Higgs doublet scalar sector at the electroweak scale as well as tree-level hierarchies in the light fermion spectra consistent with those observed in nature. In addition, our framework reveals a variety of prospects for New Physics searches at the LHC and future colliders such as vector-like fermions, as well as rich scalar, gauge and neutrino sectors.
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