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 $M^4\times T^2/\mathbb{Z}_2$. 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.
We propose a new grand unification scenario for ensuring proton stability and triplet-doublet Higgs mass splitting with the help of topological symmetry and dynamics.
Grand gauge-Higgs unification of five dimensional SU(6) gauge theory on an orbifold $S^1/Z_2$ with localized gauge kinetic terms is discussed. The Standard model (SM) fermions on the boundaries and some massive bulk fermions coupling to the SM fermions on the boundary are introduced. Taking the power-law running contributions from the bulk fields into account, perturbative gauge coupling unification is shown to be realized at around $10^{14}$ GeV, which is a few order smaller than the unification scale of four dimensional grand unified theories.
$SO(11)$ 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.
Proton hexality is a discrete symmetry that avoids the problem of too fast proton decay in the supersymmetric extension of the standard model. Unfortunately it is inconsistent with conventional grand unification. We show that proton hexality can be incorporated in the scheme of "Local Grand Unification" discussed in the framework of model building in (heterotic) string theory.
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 family unification in grand unified theory (GUT) based on an $SU(19)$ GUT gauge group broken to its subgroups including a special subgroup. In the $SU(19)$ GUT on the six-dimensional (6D) orbifold space $M^4\times T^2/\mathbb{Z}_2$, three generations of the 4D SM Weyl fermions can be embedded into a 6D bulk Weyl fermions in an $SU(19)$ second-rank anti-symmetric tensor representation. 6D and 4D gauge anomalies can be canceled out by considering proper matter content without 4D exotic chiral fermions at low energies.
The possibility of achieving a gauge coupling grand unification by increasing the QCD degrees of freedom at higher energies is investigated. When confronted with precision low-energy data, the generic weak-mixing angle relation sin^2(theta_W) = N/2(N+1) requires N=7 colors at the GUT scale M_U ~ 10^17 GeV. With the exclusive addition of light Higgs doublets to the standard model particle content, such a unification may also occur if N=5 at M_U ~ 10^16 GeV.
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 contribu…
In grand unified theories with large numbers of fields, renormalization effects significantly modify the scale at which quantum gravity becomes strong. This in turn can modify the boundary conditions for coupling constant unification, if higher dimensional operators induced by gravity are taken into consideration. We show that the generic size of these effects from gravity can be larger than the two-loop corrections typically considered in renormalization group analyses of unification. In some cases, gravitational effects of modest size can render unification impossible.
It is commonly believed that grand unified theories (GUTs) predict proton decay. This is because the exchange of extra GUT gauge bosons gives rise to dimension 6 proton decay operators. We show that there exists a class of GUTs in which these operators are absent. Many string and supergravity models in the literature belong to this class.
$SO(11)$ gauge-Higgs grand unification in the Randall-Sundrum warped space is proposed. Orbifold boundary conditions and one brane scalar field reduce $SO(11)$ to the standard model symmetry, which is further broken to $SU(3)_C \times U(1)_{EM}$ by the Hosotani mechanism. In a minimal model quarks and leptons are contained in a multiplet in ${\bf 32}$ of $SO(11)$ in each generation. Proton decay is naturally suppressed by a conserved fermion number.
In the standard model matter fields form complete representations of a grand unified group whereas Higgs fields belong to incomplete `split' multiplets. This remarkable fact is naturally explained by `local grand unification' in higher-dimensional extensions of the standard model. Here, the generations of matter fields are localized in regions of compact space which are endowed with a GUT gauge symmetry whereas the Higgs doublets are bulk fields. We realize local grand unification in the framework of orbifold compactifications of the heterotic string, and we present an example with SO(10) as a…
Supersymmetry and Grand Unification are the two most promising directions for physics beyond the Standard Model. They receive indirect experimental support from the apparent lightness of the Higgs boson, the values of the gauge couplings measured at LEP and elsewhere, and the persistent solar neutrino deficit. Phenomenological constraints and theoretical models constrain predictions in interesting ways. All these ideas may be embedded in string theory, which is shown by newly-discovered dualities to possess previously-unsuspected richness and simplicity.
The merging of the running couplings constants of the weak, strong, and electromagnetic fields does not require the unification of these gauge fields at high energy. It can, in fact, be the property of a general fermionic system in which gauge bosons are not fundamental.
Grand unified models in four dimensions typically suffer from the doublet-triplet splitting problem. This obstacle can be overcome in higher-dimensional settings, where a non-trivial gauge group topography can explain the simultaneous appearance of complete standard model generations in the form of 16-plets of SO(10) and the Higgs fields as split multiplets. In these notes, the emerging scheme of `local grand unification' and its realization in the context of orbifold compactifications of the heterotic string are reviewed.
In grand unified theories with large numbers of fields, renormalization effects significantly modify the scale at which quantum gravity becomes strong. This in turn can modify the boundary conditions for coupling constant unification, if higher dimensional operators induced by gravity are taken into consideration. We show that the generic size of, and the uncertainty in, these effects from gravity can be larger than the two-loop corrections typically considered in renormalization group analyses of unification. In some cases, gravitational effects of modest size can render unification impossibl…
We compute the beta-functions of the standard model formulated on a noncommutative spacetime. If we assume that the scale for spacetime noncommutativity is of the order of 2.2 \times 10^{15} GeV we find that the three gauge couplings of the standard model merge at a scale of 2.3 \times 10^{17} GeV. The proton lifetime is thus much longer than in conventional unification models.
Grand gauge-Higgs unification of five dimensional SU(6) gauge theory on an orbifold $S^1 / Z_2$ with localized gauge kinetic terms is discussed. The Standard model (SM) fermions on the boundaries and some massive bulk fermions coupling to the SM fermions are introduced. The number of the bulk fermions is reduced compared to the previous model, which reproduces the generation mixing of the SM fermions in addition to the SM fermion mass hierarchy by mild tuning the bulk masses and parameters of the localized gauge kinetic terms.
To solve the doublet-triplet splitting problem in SU(5) grand unified theories, we propose a four dimensional orbifold grand unified theory by acting Z2 on the SU(5) gauge group. Without an adjoint Higgs, the orbifold procedure breaks the SU(5) gauge symmetry down to the standard model gauge group, and removes the triplet component of the fundamental SU(5) Higgs. In the supersymmetric framework, we show that the orbifold procedure removes two triplet superfields of the Higgs multiplets and leaves us with the minimal supersymmetric standard model, which also solves the hierarchy problem and rea…
It has been recently pointed out by Arkani-Hamed and Dimopoulos that if the universe is a landscape of vacua, and if therefore fine-tuning is not a valid guidance principle for searching for physics beyond the standard model, supersymmetric unification only requires the fermionic superpartners. We argue that in that landscape scenario, the fermionic superpartners are not needed for unification, which can be achieved in SO(10) either via a direct breaking to the standard model at the grand unification scale or through an intermediate gauge symmetry. In most minimal SO(10) models, the proton lif…
We propose a new grand unification scenario for ensuring proton stability. Our scenario is based on the idea that the proton decay problem is an artificial one, which is caused from the identification of the gauge coupling unification scale with the grand unification scale or the grand unified symmetry breaking scale. We discuss a Lifshitz type gauge theory as a candidate to realize our scenario.
National Taiwan University（台湾大学）；National Center for Theoretical Sciences（国家理论科学中心）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学 Kavli宇宙粒子与宇宙学前沿研究所（WPI））；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Henan Normal University（河南师范大学）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
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.
We construct a simple model of an SU(5) GUT with gauge mediated supersymmetry breaking from a metastable vacuum of a hidden sector. All mass parameters and hierarchies of our model are generated dynamically from retrofitting. This includes the mu-parameter and the GUT scale. However, as typical for SU(5) GUTs, proton longevity remains a problem.
Using properties of Goldstino, we show that in generic grand unified theories with gravity-mediated supersymmetry breaking the $μ$-problem is non-existent. What happens is that supersymmetry breaking universally induces the shifts of the heavy fields that generate $μ$ and $B_μ$ terms. In the leading order, these are given by the mass of gravitino and are insensitive to the scale of grand unification. The mechanism works regardless whether doublet-triplet splitting is achieved via fine-tuning or not. Moreover, we illustrate this general phenomenon on explicit examples of theories that achieve d…
We systematically study the unification of gauge couplings in the presence of (one or more) effective dimension-5 operators cHGG/4MPl, induced into the grand unified theory by gravitational interactions at the Planck scale MPl. These operators alter the usual condition for gauge coupling unification, which can, depending on the Higgs content H and vacuum expectation value, result in unification at scales MX significantly different than naively expected. We find non-supersymmetric models of SU(5) and SO(10) unification, with natural Wilson coefficients c, that easily satisfy the constraints fro…
We obtain a supersymmetric three family chiral SU(6) grand unification model with the global family symmetry SU(3)[family] from F-theory. This model has nice features such as all the fermion masses are reasonably generated and there results only one pair of Higgs doublets, realizing the doublet-triplet splitting from the family symmetry SU(3)[family]. The proton hexality is realized toward the proton stability problem. There is a room to fit the three gauge couplings using the F-theory flux idea and we obtain the proton lifetime in the 10^{36-37} yr region.
We review several problems of conventional Grand Unification and some new approaches. In particular, we discuss strongly coupled Grand Unified Theories. Standard Model may emerge as a low energy effective theory of composite particles in these models. We construct a realistic model of this kind.
One of the drawbacks of conventional grand unification scenarios has been that the unification scale is too high to permit direct exploration. In this paper, we show that the unification scale can be significantly lowered (perhaps even to the TeV scale) through the appearance of extra spacetime dimensions. Such extra dimensions are a natural consequence of string theories with large-radius compactifications. We show that extra spacetime dimensions naturally lead to gauge coupling unification at intermediate mass scales, and moreover may provide a natural mechanism for explaining the fermion ma…
We discuss a grand unified theory (GUT) based on an $SO(32)$ GUT gauge group broken to its subgroups including a special subgroup. In the $SO(32)$ GUT on six-dimensional (6D) orbifold space $M^4\times T^2/\mathbb{Z}_2$, one generation of the SM fermions can be embedded into a 6D bulk Weyl fermion in the $SO(32)$ vector representation. We show that 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.
A possibility for grand unification and non-Higgs mass generation in a Nambu-Jona-Lasinio-like theory of fermions interacting with current metric field
The mass spectra of the standard model particles are reproduced in the $SO(11)$ gauge-Higgs grand unification in the six-dimensional warped space without introducing exotic light fermions. Light neutrino masses are explained by the gauge-Higgs seesaw mechanism. We evaluate the effective potential of the 4d Higgs boson appearing as a fluctuation mode of the Aharonov-Bohm phase $θ_H$ in the extra-dimensioal space, and show that the dynamical electroweak symmetry breaking takes place with the Higgs boson mass $m_H \sim 125\,$GeV and $θ_H \sim 0.1$. The Kaluza-Klein mass scale in the fifth dimensi…
We present a new grand unification paradigm, where gauge couplings do not need to be equal at any given scale, instead they run towards the same fixed point in the deep ultraviolet. We provide a concrete example based on SU(5) with a compactified extra space dimension. By construction, fermions are embedded in different SU(5) bulk fields, hence baryon number is conserved and proton decay is forbidden. The lightest Kaluza-Klein tier consists of stable states, providing an asymmetric Dark Matter candidate via their baryonic charges, with a mass of 2.4 TeV. The model features an interesting and p…
We consider Grand Unified Theories based on $SO(10)$ which originate from string/$M$ theory on $G_2$ manifolds or Calabi-Yau spaces with discrete symmetries. In this framework we are naturally led to a novel solution of the doublet-triplet splitting problem previously considered by Dvali which involves an extra vector-like Standard Model family and light, but weakly coupled colour triplets. These additional states are predicted to be accessible at the LHC and also induce R-parity violation. Gauge coupling unification occurs with a larger GUT coupling.
We analyze the running at one-loop of the gauge couplings in the spectral Pati-Salam model that was derived in the framework of noncommutative geometry. There are a few different scenario's for the scalar particle content which are determined by the precise form of the Dirac operator for the finite noncommutative space. We consider these different scenarios and establish for all of them unification of the Pati-Salam gauge couplings. The boundary conditions are set by the usual RG flow for the Standard Model couplings at an intermediate mass scale at which the Pati-Salam symmetry is broken.
We discuss new-type grand unified theories based on grand unified groups broken to their special subgroups as well as their regular subgroups. In the framework, when we construct four-dimensional (4D) chiral gauge theories, i.e., the Standard Model (SM), 4D gauge anomaly cancellation restricts the minimal number of generations of the 4D SM Weyl fermions. We show that in a six-dimensional (6D) $SU(16)$ gauge theory on $M^4\times T^2/\mathbb{Z}_2$ one generation of the SM fermions can be embedded into a 6D bulk Weyl fermion. For the model including three chiral generations of the SM fermions, th…
We consider Grand Unified Theories based on $SO(10)$ which originate from $M$ theory on $G_2$ manifolds. In this framework we are naturally led to a novel solution of the doublet-triplet splitting problem involving an extra $\overline{\bf 16}_X+{\bf 16}_X$ vector-like pair by considering discrete symmetries of the extra dimensions and preserving unification. Since Wilson line breaking preserves the rank of the gauge group, the necessary $U(1)$ gauge breaking is generated from extra multiplets. The main prediction of the approach is the existence of light states with the quantum numbers of a $\…
We present a framework for grand unification in which the grand unified symmetry is broken spontaneously by strong gauge dynamics, and yet the physics at the unification scale is described by (weakly coupled) effective field theory. These theories are formulated, through the gauge/gravity correspondence, in truncated 5D warped spacetime with the UV and IR branes setting the Planck and unification scales, respectively. In most of these theories, the Higgs doublets arise as composite states of strong gauge dynamics, corresponding to degrees of freedom localized to the IR brane, and the observed …
Requiring that supersymmetric SU(5) and SU(6) grand unifications in the heterotic string theory must have 3 chiral families, adjoint (or higher representation) Higgs fields in the grand unifiedgauge group, and a non-abelian hidden sector, we construct such string models within the framework of conformal field theory and asymmetric orbifolds. Within this framework, we construct all such string models via Z_6 asymmetric orbifolds that include a Z_3 outer-automorphism, the latter yielding a level-3 current algebra for the grand unification gauge group SU(5) or SU(6). We then classify all such Z_6…
We present a minimal model of asymptotic grand unification based on an $SU(5)$ gauge theory in a compact $S^1/(\mathbb{Z}_2 \times \mathbb{Z}'_2)$ orbifold. The gauge couplings run to a unified fixed point in the UV, without supersymmetry. By construction, fermions are embedded in different $SU(5)$ bulk fields. As a consequence, baryon number is conserved, thus preventing proton decay, and the lightest Kaluza-Klein tier consists of new states that cannot decay into standard model ones. We show that the Yukawa couplings can be either in the bulk or localized, and run to an asymptotically free f…
Recent progress in some selected areas of grand unification and physics beyond the standard model is reviewed. Topics include gauge coupling unification, SU(5), SO(10), symmetry breaking mechanisms, finite field theory: SU(3)^3, leptonic color: SU(3)^4, chiral color and quark-lepton nonuniversality: SU(3)^6.
The grand unification scale $M_{GUT}\sim 10^{16}$ GeV may arise from dynamical effects. With the advances in understanding of supersymmetric dynamics, we can break the grand unified group by introducing a strong gauge group which generates the grand unification scale. We also show how this mechanism can be combined with solutions to the doublet-triplet splitting problem. The same method can also be used for other symmetry breakings at intermediate scales as well.
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 show that an intermediate gauge symmetry breaking scale can be a significant source of electric dipole moments for the electron and neutron in supersymmetric grand unified theories. New phases, similar to that of the CKM matrix, appear which do not arise from the supersymmetry (SUSY) breaking operators. To illustrate, we choose some grand unified SUSY models having an intermediate gauge symmetry breaking scale with some attractive features. We also show how well the $b-τ$ unification hypothesis works in this class of models.
We discuss the production of lepton flavor violation and EDMs and the viability of the $b-τ$ unification hypothesis in SUSY grand unification with an intermediate gauge symmetry breaking scale.
The grand unification of flavor(GUF) in extra dimensions is discussed. After reviewing the old GUF, I present a GUF model SU(7) in 5D with the recently popular field theoretic orbifold compactification.
In the recent successful applications of the non-Abelian discrete symmetry A_4 to the tribimaximal mixing of neutrinos, lepton doublets and singlets do not transform in the same way. It appears thus to be unsuitable as a family symmetry in grand unification. A simple resolution of this dilemma is proposed.
We consider constraints on gauge mediated supersymmetry breaking models imposed by the requirement of grand unification. In particular, we demonstrate several ways to reduce the number of parameters coming from the dynamical supersymmetry breaking sector. One of approaches exploits nonperturbative unification of gauge couplings in multi-messenger models.
Data on solar and atmospheric neutrinos provide evidence for neutrino masses and mixings. We review some basic neutrino properties, the status of neutrino oscillations and implications for grand unified theories, including leptogenesis.
We consider first heavy particles with masses $M\sim M_{GUT}$ which arise in the Universe during phase transitions at the Grand Unification scale. Using statistical mechanics approach we show that they behave like ideal quantum degenerate Bose gas which has the temperature of the Hawking thermal radiation due to presence of the de Sitter event horizon. The equation of state for both scalar and gauge bosons is presented including the coupling constant at the Grand Unification scale.
The current status of gauge unification is surveyed both in the standard model and its minimal supersymmetric extension. Implications for proton decay, Yukawa unification, and the Higgs mass are described.
If a grand-unified extension of the asymptotically safe Reuter fixed-point for quantum gravity exists, it determines free parameters of the grand-unified scalar potential. All quartic couplings take their fixed-point values in the trans-Planckian regime. They are irrelevant parameters that are, in principle, computable for a given particle content of the grand unified model. In turn, the direction of spontaneous breaking of the grand-unified gauge symmetry becomes predictable. For the flow of the couplings below the Planck mass, gauge and Yukawa interactions compete for the determination of th…
We study the evolution of fermion mass matrices considering the hypothesis of approximate flavor symmetries (AFS) in the Standard Model and a two-Higgs-doublet model. We find that the hierarchical structure is not significantly altered by the running, hence the assumption of AFS is entirely compatible with a grand unification scenario.
