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A grand unification scenario is presented that is based on quantum field theory, and where a single [Formula: see text] gauge superfield in 10 dimensions is used to obtain all the particle content of the Standard Model at low energies. The key feature of the formulation lies in the dimensional reduction used to break the gauge symmetry and to determine the low energy spectrum. It is shown that, through the orbifold [Formula: see text], and its corresponding Wilson lines, the symmetry is broken to the Standard Model one, generating a particular model that includes the Minimal Supersymmetric Standard Model spectrum. Furthermore it is also shown that the model is free of gauge anomalies at all levels by itself, i.e. without the need to include any additional representations of fields. Thus a complete unification of the Standard Model into a single gauge superfield is shown to be formally plausible. Although this paper does not include a phenomenological study of the specific model (currently being investigated), some interesting questions and observations are included as motivation for the scenario.

Grand unification groups (GUTs) are constructed from SO(32) heterotic string via $\Z_{12-I}$ orbifold compactification. So far, most phenomenological studies from string compactification relied on $\EE8$ heterotic string, and this invites the SO(32) heterotic string very useful for future phenomenological studies. Here, spontaneous symmetry breaking is achieved by Higgsing of the anti-symmetric tensor representations of SU($N$). The anti-SU($N$) presented in this paper is a completely different class from the flipped-SU($N$)s from the spinor representations of SO($2N$). Here, we realize chiral representations: $\tsix\oplus 5\cdot\nineb $ for a SU(9) GUT and $3\{{\ten}'_L\oplus {\fiveb}'_L\}$ for a SU(5)$'$ GUT. In particular, we confirm that the non-Abelian anomalies of SU(9) gauge group vanish and hence our compactification scheme achieves the key requirement. We also present the Yukawa couplings, in particular for the heaviest fermion, $t$, and lightest fermions, neutrinos. In the supersymmetric version, we present a scenario how supersymmetry can be broken dynamically via the confining gauge group SU(9). Three families in the visible sector are interpreted as the chiral spectra of SU(5)$'$ GUT., Comment: 20 pages, no figure

In this short note, we will prove in a few steps that the new tetrads introduced previously in Einstein–Maxwell four-dimensional Lorentzian spacetimes, where gravitational and non-null electromagnetic fields are present, contain both the necessary information to provide the gravitational field and the necessary information to provide the electromagnetic field as well. These new tools thus become grand unification objects.

Advances in high intensity beams have driven particle physics forward since the inception of the field. State-of-the-art and next generation high intensity beams will drive experiments searching for ultrarare processes sensitive through quantum corrections to new particle states far beyond the reach of direct production in foreseeable beam colliders. The recent discovery of the ultrarare B meson decay Bs → μμ, with a branching fraction of 3 × 10-9 for example, has set stringent limits on new physics within direct reach of the Large Hadron Collider. Today, even in the context of the Higgs boson discovery, observation of finite neutrino masses is the only laboratory evidence of physics beyond the Standard Model of particle physics. The tiny mass scale of neutrinos may foretell and one day expose physics that connects quarks and leptons together at the "grand unification" scale and may be the portal through which our world came to the matter-dominated state so different from conditions we expect in the early universe. Here we describe next generation neutrino and rare processes experiments that will deeply probe these and other questions central to the field of particle physics.

We discuss how a model for the electroweak interactions without a Higgs could be embedded into a grand unified theory. The requirement of a non-trivial fixed point in the SU(2) sector of the weak interactions together with the requirement of the numerical unification of the gauge couplings leads to a prediction for the value of the SU(2) gauge coupling in the fixed point regime. The fixed point regime must be in the TeV region to solve the unitarity problem in the elastic scattering of W bosons. We find that the unification scale is at about 10^{14} GeV. Viable grand unified theories must thus conserve baryon number. We discuss how to build such a model without using Higgs bosons., Comment: 8 pages, to be published in the proceedings devoted to the Scientific and Human Legacy of Julius Wess, initiated by the JW2011 Workshop, August 27 - 28, 2011, Donji Milanovac, Serbia

Polyvector-valued gauge field theories in Clifford spaces are used to construct a novel Cl (3, 2) gauge theory of gravity that furnishes modified curvature and torsion tensors leading to important modifications of the standard gravitational action with a cosmological constant. Vacuum solutions exist which allow a cancelation of the contributions of a very large cosmological constant term and the extra terms present in the modified field equations. Generalized gravitational actions in Clifford-spaces are provided and some of their physical implications are discussed. It is shown how the 16 fermions and their masses in each family can be accommodated within a Cl (4) gauge field theory. In particular, the Higgs fields admit a natural Clifford-space interpretation that differs from the one in the Chamseddine–Connes spectral action model of non-commutative geometry. We finalize with a discussion on the relationship with the Pati–Salam color-flavor model group SU (4)C × SU (4)F and its symmetry breaking patterns. An Appendix is included with useful Clifford algebraic relations.

The understanding about the creation of our universe is explored in many philosophies, natural sciences, religions, ideologies, traditions and many other disciplines. Currently, natural science cannot answer this question at the most fundamental level. In this work, based on the ancient Chinese Tao wisdom about creation, we propose the Law of Tao Yin–Yang Creation. This law states that everything is created from emptiness through yin–yang interaction. Yin and yang are the two basic elements that make up everything. Yin and yang are opposite, relative, co-created, inseparable and co-dependent. The Law of Tao Yin–Yang Creation gives us a deeper insight about space and time. We propose that space and time are two basic measurements we conduct. Time relates to the measurement of movement and change. Space relates to the measurement of stillness and solidity. Space and time are a yin–yang pair. Interaction of two fundamental yin–yang pairs, the space and time yin–yang pair and the inclusion and exclusion duality pair, create our universe. We demonstrate that from this insight, one can derive string theory, superstring or M-theory and the universal wave function interpretation of string theory. We suggest that the Law of Tao Yin–Yang Creation presents the exact process how “it from bit” and it could be the fundamental principle leading to the grand unification theory and the theory of everything.

We study the mass ratio of W and Z bosons in an SU(5) gauge-Higgs unification model with the left-right symmetry remaining locally for boundary conditions and with no scalar fields except for the extra-dimensional component of gauge bosons. We find that there are a variety of boundary conditions to yield distinct values of the mass ratio., Comment: 22 pages

It is shown how a conformal gravity and U (4) × U (4) Yang–Mills grand unification model in four dimensions can be attained from a Clifford gauge field theory in C-spaces (Clifford spaces) based on the (complex) Clifford Cl (4, C) algebra underlying a complexified four-dimensional space–time (eight real dimensions). Upon taking a real slice, and after symmetry breaking, it leads to ordinary gravity and the Standard Model in four real dimensions. A brief conclusion about the noncommutative star-product deformations of this Grand Unified Theory of gravity with the other forces of Nature is presented.

A candidate action for an Exceptional E8 gauge theory of gravity in 8D is constructed. It is obtained by recasting the E8 group as the semi-direct product of GL(8,R) with a deformed Weyl–Heisenberg group associated with canonical-conjugate pairs of vectorial and antisymmetric tensorial generators of rank two and three. Other actions are proposed, like the quarticE8 group-invariant action in 8D associated with the Chern–Simons E8 gauge theory defined on the 7-dim boundary of a 8D bulk. To finalize, it is shown how the E8 gauge theory of gravity can be embedded into a more general extended gravitational theory in Clifford spaces associated with the Cl(16) algebra and providing a solid geometrical program of a grand unification of gravity with Yang–Mills theories. The key question remains if this novel gravitational model based on gauging the E8 group may still be renormalizable without spoiling unitarity at the quantum level.

The paper presents a summary of some recent work on a SU(5) grand unification scheme for effective 3 + 1 dimensional fields dynamically localized on a domain-wall brane. This is achieved through the confluence of the clash-of-symmetries mechanism for symmetry breaking through domain-wall formation and the Dvali-Shifman gauge boson localization idea. It is shown that it requires an E6 invariant action, yielding a domain-wall solution that has E6 broken to differently embedded SO(10) ⊗ U(1) subgroups in the two bulk regions on the opposites of the wall.

We investigate the prediction on the lepton phases in theories with a non trivial correlation between quark (CKM) and lepton (PMNS) mixing matrices. We show that the actual evidence, under the only assumption that the correlation matrix $V^M$ product of $CKM$ and $PMNS$ has a zero in the entry $(1,3)$, gives us a prediction for the three CP-violating invariants $J$, $S_1$, and $S_2$. A better determination of the lepton mixing angles will give a strong prediction of the CP-violating invariants in the lepton sector. These will be tested in the next generation experiments. To clarify how our prediction works, we show how a model based on a Grand Unified Theory and the permutation flavor symmetry $S_3$ predicts $V^M_{13}=0$., Comment: 7 pages, 3 figures. V2: new figure added

I discuss the possibility of generating the observed baryon number in the universe through the lepton-number violating processes in a class of SO(10) grand unification theories. The key ingredient is the CP violating decay of the heavy right-handed neutrinos out of thermal equilibrium.

The hypothesis that dark matter consists of superheavy particles with the mass close to the Grand Unification scale is investigated. These particles were created from vacuum by the gravitation of the expanding Universe and their decay led to the observable baryon charge. Some part of these particles with the lifetime larger than the time of breaking of the Grand Unification symmetry became metastable and survived up to the modern time as dark matter. However in active galactic nuclei due to large energies of dark matter particles swallowed by the black hole the opposite process can occur. Dark matter particles become interacting. Their decay on visible particles at the Grand Unification energies leads to the flow of ultra high energy cosmic rays observed by the Auger group. Numerical estimates of the effect leading to the observable numbers are given., Comment: LATEX, 5 pages, no figure

This talk consists of two parts. In part I we review how the minimal renormalizable supersymmetric SO(10) model, an SO(10) framework with only one 10 and one 126 Higgs multiplets in the Yukawa sector, is attractive because of its highly predictive power. Indeed it not only gives a consistent predictions on neutrino oscillation data but also gives reasonable and interesting values for leptogenesis, LFV, muon g-2, neutrinoless double beta decay etc. However, this model suffers from problems related to running of gauge couplings. The gauge coupling unification may be spoiled due to the presence of Higgs multiplets much lighter than the grand unification (GUT) scale. In addition, the gauge couplings blow up around the GUT scale because of the presence of Higgs multiplets of large representations. In part II we consider the minimal SO(10) model in the warped extra dimension and show a possibility to solve these problems., Comment: 15 pages, 7 figures, Talk given at the International Workshop on Neutrino Masses and Mixings Toward Unified Understanding of Quarks and Lepton Mass Matrices, held at University of Shizuoka on December 17-19, 2006

The so-called Stueckelberg transformation is introduced as a prescription of minimal coupling following the procedure of the Utiyama theory, for both internal and spacetime symmetry Lie groups. As a natural example, the theory is applied to the Weyl group and the corresponding gauge gravitational theory is developed. This context appears to be a natural source to account for some sort of dark matter intrinsically related to the gauge-group parameter associated with scale transformations.

In the first part of the talk, I explain what empirical evidence points to the need for having an effective grand unification-like symmetry possessing the symmetry SU(4)-color in 4D. If one assumes the premises of a future predictive theory including gravity--be it string/M theory or a reincarnation--this evidence then suggests that such a theory should lead to an effective grand unification-like symmetry as above in 4D, near the string-GUT-scale, rather than the standard model symmetry. Advantages of an effective supersymmetric G(224) = SU(2)$_L \times$ SU(2)$_R \times$ SU(4)$^c$ or SO(10) symmetry in 4D in explaining (i) observed neutrino oscillations, (ii) baryogenesis via leptogenesis, and (iii) certain fermion mass-relations are noted. And certain distinguishing tests of a SUSY G(224) or SO(10)-framework involving CP and flavor violations (as in $\mu \to e\gamma$, $\tau \to\mu\gamma$, edm's of the neutron and the electron) as well as proton decay are briefly mentioned. Recalling some of the successes we have had in our understanding of nature so far, and the current difficulties of string/M theory as regards the large multiplicity of string vacua, some comments are made on the traditional goal of understanding {\em vis a vis} the recently evolved view of landscape and anthropism., Comment: A chart showing some insights gained in the world of the very small and that of the very large is included. A few relevant references are added. Some clarification is made in the last section as regards the question of understanding versus landscape and anthropism

We demonstrate to two-loop order that an intermediate symmetrically embedded Pati-Salam $SU(2)_L \times SU(2)_R \times SU(4)$ level of symmetry is all that is necessary to accommodate empirical values of $\alpha(M_z), \alpha_s(M_z)$ and $\sin^2\theta_w(M_z)$ within a grand unification context but with a high (10^{14} GeV) intermediate mass scale and with a concomitant higher GUT scale., Comment: 7 pages, 4 embedded eps figure

This review is devoted to the Multiple Point Principle (MPP), according to which several vacuum states with the same energy density exist in Nature. The MPP is implemented to the Standard Model (SM), Family replicated gauge group model (FRGGM) and phase transitions in gauge theories with/without monopoles. Lattice gauge theories are reviewed. The lattice results for critical coupling constants are compared with those of the Higgs Monopole Model (HMM), in which the lattice artifact monopoles are replaced by the point-like Higgs scalar particles with a magnetic charge. Considering our (3+1)-dimensional space-time as discrete, for example, as a lattice with a parameter a=\lambda_P, equal to the Planck length, we have investigated the additional contributions of monopoles to beta-functions of renormalization group equations in the FRGGM extended beyond the SM at high (the Planck scale) energies. We have reviewed that, in contrast to the Anti-grand unified theory (AGUT), there exists a possibility of unification of all gauge interactions (including gravity) near the Planck scale due to monopoles. The unifications [SU(5)]^3 and [SO(10)]^3 at the GUT-scale \sim 10^{18} GeV are briefly discussed., Comment: 100 pages, 25 figures, typos corrected

We present a geometrical unification theory in a Kaluza-Klein approach that achieve the geometrization of a generic gauge theory bosonic component. We show how it is possible to derive the gauge charge conservation from the invariance of the model under extra-dimensional translations and to geometrize gauge connections for spinors, thus we can introduce the matter just by free spinorial fields. Then, we present the applications to i)a pentadimensional manifold $V^{4}\otimes S^{1}$, so reproducing the original Kaluza-Klein theory, unless some extensions related to the rule of the scalar field contained in the metric and the introduction of matter by spinors with a phase dependence from the fifth coordinate, ii)a seven-dimensional manifold $V^{4}\otimes S^{1}\otimes S^{2}$, in which we geometrize the electro-weak model by introducing two spinors for any leptonic family and quark generation and a scalar field with two components with opposite hypercharge, responsible of spontaneous symmetry breaking., Comment: 37 pages, no figures

This review intends to introduce the reader to the general methodology of computing GUT particle spectrum from compactifying the E8 × E8 heterotic string on smooth Calabi–Yau threefolds endowed with stable vector bundles. We use the spectral construction for the bundle and show, with illustrative examples, how one computes the requisite cohomology groups that determine the spectrum. Moreover, physical constraints lead to an algorithmic classification scheme. Finally, we will see the fascinating moduli-dependence, a so-called jumping phenomenon, of the particle spectra.

Unification of electromagnetic, weak, and strong coupling constants is studied in the extension of standard model with additional fermions and scalars. It is remarkable that this unification in the supersymmetric extension of standard model yields a value of Weinberg angle which agrees very well with experiments. We discuss the other possibilities which can also give same result., 13 pages, equations, additional references added

A brief review is given of some ideas for explaining neutrino masses and mixings within the context of supersymmetric grand unification. Emphasis is put on so-called lopsided models.

We revisit the issue of the vacuum angle [Formula: see text] dependence in weakly coupled (Higgsed) Yang–Mills theories. Two most popular mechanisms for eliminating physical [Formula: see text] dependence are massless quarks and axions. Anselm and Johansen noted that the vacuum angle [Formula: see text], associated with the electroweak SU(2) in the Glashow–Weinberg–Salam model (Standard Model, SM), is unobservable although all fermion fields obtain masses through Higgsing and there is no axion. We generalize this idea to a broad class of Higgsed Yang–Mills theories. In the second part, we consider the consequences of Grand Unification. We start from a unifying group, e.g. SU(5), at a high ultraviolet scale and evolve the theory down within the Wilson procedure. If on the way to infrared the unifying group is broken down into a few factors, all factor groups inherit one and the same [Formula: see text] angle — that of the unifying group. We show that embedding the SM in SU(5) drastically changes the Anselm–Johansen conclusion: the electroweak vacuum angle [Formula: see text], equal to [Formula: see text] becomes in principle observable in [Formula: see text] processes. We also note in passing that if the axion mechanism is set up above the unification scale, we have one and the same axion in the electroweak theory and QCD, and their impacts are interdependent.

As a tribute to Abdus Salam, I recall the initiation in 1972-73 of the idea of grand unification based on the view that lepton number is the fourth color. Motivated by aesthetic demands, these attempts led to the suggestion that the existing $SU(2)\times U(1)$ symmetry be extended minimally to the quark-lepton and left-right symmetric non-Abelian gauge structure $G(2,2,4) = SU(2)_L\times SU(2)_R\times SU(4)$-color. This unified members of a family within a single L-R self-conjugate multiplet. It also explained: the quantization of electric charge, the co-existence of quarks and leptons, and that of their three forces, while providing the appealing possibility that nature is fundamentally left-right symmetric. The minimal extension of $G(2,2,4)$ to a simple group is given by the symmetry $SO(10)$ that came a year later. The advantages of the core symmetry $G(2,2,4)$, including those listed above (which are of course retained by $SO(10)$), are noted. These include the introductions of: (i){ \it the right-handed neutrino as a compelling member of each family}, (ii) (B-L) as a local symmetry, and (iii) the relation $ m(\nu^\tau)_{Dirac} = m_{top}$. These three features, as well as the gauge coupling unification scale, are crucially needed to understand the tiny mass-scales of the neutrino oscillations within the seesaw mechanism, and to implement successfully the mechanism of baryogenesis via leptogenesis. Implications of a well-motivated class of models based on supersymmetric $SO(10)$ or a string-unified $G(2,2,4)$ symmetry in 4D for (a) gauge coupling unification, (b) fermion masses and mixings, (c) neutrino osillations, (d) baryogenesis via leptogenesis, and last but not least (e) proton decay are presented. Recent works on the latter providing upper limits on proton lifetimes suggest that the potential for discovery of proton decay in the next-generation detectors would be high., Comment: Presented at the Abdus Salam 90th birthday Memorial Meeting, IAS, Singapore, January 25-28, 2016

We study emergent Yang–Mills theories which could origin from universal extra dimensions. Particularly, some vector field potential terms or polynomial vector field constraints introduced into five-dimensional (5D) non-Abelian gauge theory is shown to lead to spontaneous violation of an underlying spacetime symmetry and generate vector pseudo-Goldstone modes as conventional four-dimensional (4D) gauge boson candidates. As a special signature, apart from conventional gauge couplings, there appear an infinite number of the properly suppressed direct multi-boson (multi-photon in particular) interaction couplings in emergent Yang–Mills theories whose observation could shed light on their high-dimensional nature. Moreover, in these theories, an internal symmetry also appeared spontaneously broken to its diagonal subgroups. This breaking originates from the extra vector field components playing the role of some adjoint scalar field multiplet in the 4D spacetime. So, one naturally has the Higgs effect without a specially introduced scalar field multiplet. Remarkably, when applied to Grand Unified Theories (GUTs), this results in an automatic breakdown of emergent GUTs down to the Standard Model (SM) just at the 5D Lorentz violation scale M.

Recent measurements of temperature fluctuations in the cosmic microwave background (CMB) indicate that the Universe is flat and that large-scale structure grew via gravitational infall from primordial adiabatic perturbations. Both of these observations seem to indicate that we are on the right track with inflation. But what is the new physics responsible for inflation? This question can be answered with observations of the polarization of the CMB. Inflation predicts robustly the existence of a stochastic background of cosmological gravitational waves with an amplitude proportional to the square of the energy scale of inflation. This gravitational-wave background induces a unique signature in the polarization of the CMB. If inflation took place at an energy scale much smaller than that of grand unification, then the signal will be too small to be detectable. However, if inflation had something to do with grand unification or Planck-scale physics, then the signal is conceivably detectable in the optimistic case by the Planck satellite, or if not, then by a dedicated post-Planck CMB polarization experiment. Realistic developments in detector technology as well as a proper scan strategy could produce such a post-Planck experiment that would improve on Planck's sensitivity to the gravitational-wave background by several orders of magnitude in a decade timescale., Comment: 13 page, 4 figures. To appear in the proceedings of DPF2000, Columbus, 9-12 August 2000 and (with slight revisions) in the proceedings of, "Gravitational Waves: A Challenge to Theoretical Astrophysics," Trieste, 5-9 June 2000

A supersymmetric vector-like standard model without leptons is suggested to investigate the unification between gauge interactions and gravity under two-loop approximation for gauge interactions and one-loop string correction for gravitation. It is found that two intermediate mass scales are needed where the lower mass scale may be accessible in laboratory in future and the higher mass scale is of the order of 1016 GeV .

Theoretical backgound for bileptonic gauge bosons is reviewed, both the SU(15) GUT model and the 3-3-1 model. Mass limits on bileptons are discussed coming from $e^+e^-$ scattering, polarized muon decay and muonium-antimuonium conversion. Discovery in $e^-e^-$ at a linear collider at low energy (100GeV) and high luminosity ($10^{33}/cm^2/s$) is emphasised.}, 9 pages LaTeX. Talk at Third International Workshop on Electron-Electron Interactions at TeV Energies, UC-Santa Cruz. December 10-12, 1999

Generalized Yang-Mills theories have a covariant derivative that employs both scalar and vector bosons. Here we show how grand unified theories of the electroweak and strong interactions can be constructed with them. In particular the SU(5) GUT can be obtained from SU(6) with SU(5)xU(1) as a maximal subgroup. The choice of maximal subgroup also determines the chiral structure of the theory. The resulting Lagrangian has only two terms, and only two irreducible representations are needed, one for fermions and another for bosons., Comment: 10 pages, no figures

We calculate the U(1) continuum gauge coupling using the values of action parameters coinciding with the multiple point. This is a point in the phase diagram of a lattice gauge theory where a maximum number of phases convene. We obtain for the running inverse fine structure constant the values [Formula: see text] and [Formula: see text] at the Planck scale and the MZ scale, respectively. The gauge group underlying the phase diagram in which we seek multiple point parameters is what we call the Anti-grand-unified theory (AGUT) gauge group SMG 3, which is the Cartesian product of three Standard Model Groups (SMG's). There is one SMG factor for each of the N gen =3 generations of quarks and leptons. In our model, this gauge group SMG 3 is the predecessor of the usual SMG. The latter arises as the diagonal subgroup surviving the Planck scale breakdown of SMG 3. This breakdown leads to a weakening of the U(1) coupling by a N gen -related factor. For N gen =3, this factor would be N gen (N gen +1)/2=6 if phase transitions between all the phases convening at the multiple point were purely second order. The factor N gen (N gen +1)/2=6 corresponds to the six gauge-invariant combinations of the N gen =3 different U(1)'s that give action contributions that are second order in Fμν. The factor analogous to this N gen (N gen +1)/2=6 in the case of the earlier considered non-Abelian couplings reduced to the factor N gen =3 because action terms quadratic in Fμν that arise as contributions from two different of the N gen =3 SMG factors of SMG 3 are forbidden by the requirement of gauge symmetry. Actually we seek the multiple point in the phase diagram of the gauge group U(1) 3 as a simplifying approximation to the desired gauge group SMG 3. The most important correction obtained from using multiple point parameter values (in a multiparameter phase diagram instead of the single critical parameter value obtained, say, in the one-dimensional phase diagram of a Wilson action) comes from the effect of including the influence of also having at this point phases confined solely w.r.t. discrete subgroups. In particular, what matters is that the degree of first-orderness is taken into account in making the transition from these latter phases at the multiple point to the totally Coulomb-like phase. This gives rise to a discontinuity Δγ eff in an effective parameter γ eff . Using our calculated value of the quantity Δγ eff , we calculate the above-mentioned weakening factor to be more like 6.5 instead of the N gen (N gen +1)/2=6, as would be the case if all multiple point transitions were purely second order. Using this same Δγ eff , we also calculate the continuum U(1) coupling corresponding to the multiple point of a single U(1). The product of this latter and the weakening factor of about 6.5 yields our Planck scale prediction for the continuum U(1) gauge coupling, i.e. the multiple point critical coupling of the diagonal subgroup of U(1) 3∈ SMG 3. Combining this with the results of earlier work on the non-Abelian gauge couplings leads to our prediction of α-1-137 ± 9 as the value for the fine structure constant at low energies.

By way of paying tribute to Abdus Salam, I recall the ideas of higher unification that he and I initiated. I discuss the current status of those ideas in the light of recent developments, including those of: (a) gauge coupling unification, (b) discovery of neutrino-oscillation at SuperKamiokande, and (c) ongoing searches for proton decay. It is remarked that the mass of $\nu_\tau$ ($\sim$ 1/20 eV) suggested by the SuperK result seems to provide clear support for an underlying unity of forces based on the ideas of (i) SU(4)-color, (ii) left-right symmetry and (iii) supersymmetry. The change in perspective, pertaining to both gauge coupling unification and proton decay, brought forth by supersymmetry and superstrings is presented. The beneficial roles of string- symmetries in addressing certain naturalness problems of supersymmetry, including that of rapid proton decay, are noted. In the last section, attention is drawn to the recent joint works with K. Babu and F. Wilczek, where the influence of neutrino masses and thus of the new SuperK result on proton decay are noted. In this context, it is remarked that with neutrino masses and coupling unification revealed, the discovery of proton decay, that remains as the missing link, should not be far behind., Comment: Invited talk at the Abdus Salam Memorial meetimg, Trieste, November, 1997; latex, 34 pages

We study topological defects arising in the grand unification model SU (6)L⊗ SU (6)c⊗ SU (6)R× Z3. We show that the model does not contain domain walls, while it produces massive magnetic monopoles and it may, depending on the symmetry breaking chain, give rise to the formation of strings. We also discuss the possible relation of these topological defects with the origin of the highest energy cosmic rays detected.

We investigate the SO(10)-unification model in a Lie algebraic formulation of noncommutative geometry. The SO(10)-symmetry is broken by a 45-Higgs and the Majorana mass term for the right neutrinos (126-Higgs) to the standard model structure group. We study the case that the fermion masses are as general as possible, which leads to two 10-multiplets, four 120-multiplets and two additional 126-multiplets of Higgs fields. This Higgs structure differs considerably from the two Higgs multiplets 16 \otimes 16^* and 16^c \otimes 16^* used by Chamseddine and Fr\"ohlich. We find the usual tree-level predictions of noncommutative geometry m_W=(1/2)m_t, \sin^2\theta_W=(3/8) and g_2=g_3 as well as m_H \leq m_t., Comment: 25 pages, LaTeX 2e. v2: typos corrected and footnote on Super-Kamiokande results added

It is proposed that the highest energy $\sim 10^{20}$eV cosmic ray primaries are protons, decay products of a long-lived progenitor which has propagated from typically $\sim 100$Mpc. Such a scenario can occur in e.g. SU(15) grand unification and in some preon models, but is more generic; if true, these unusual cosmic rays provide a window into new physics., Comment: 8 pages, RevTeX

Future sattelite, balloon and ground based experiments will give precision determinations of the basic cosmological parameters and hence determine the amount of cold dark matter accurately. We consider here two cosmological models, the nuCDM model and the LambdaCDM model, and examine within the framework of supergravity grand unification the effect this will have for these models on supersymmetry searches at accelerators. In the former example the gluino (neutralino) mass has an upper bound of about 720(100) GeV and gaps (forbidden regions) may deveop at lower energies. In the latter case the upper bound occurs at gluino (neutralino) mass of about 520(70) GeV with squarks and selectron becoming light when gluino (neutralino) masses are greater than 420(55) GeV. Both models are sensitive to non-universal soft breaking masses, and show a correlation between large (small) dark matter detector rates and low (high) b -> s+ gamma branching ratio., RevTeX 10 pages, 4 figures

We formulate the flipped SU(5)×U(1)-GUT within a Lie-algebraic approach to non-commutative geometry. It suffices to take the matrix Lie algebra su(5) as the input; the u(1)-part with its representation on the fermions is an algebraic consequence. The occurring Higgs multiplets (24, 5, 45, 50-representations of su(5)) are uniquely determined by the fermionic mass matrix and the spontaneous symmetry breaking pattern to SU(3)C×U(1)EM. We find the most general gauge invariant Higgs potential that is compatible with the given Higgs vacuum. Our formalism yields tree-level predictions for the masses of all gauge and Higgs bosons. It turns out that the low-energy sector is identical with the standard model. In particular, there exists precisely one light Higgs field, whose upper bound for the mass is 1.45 mt. All remaining 207 Higgs fields are extremely heavy.

In a preceding paper at Foundations of Physics Letters,11 we have submitted the apparently first, axiomatically consistent inclusion of gravitation in unified gauge theories of electroweak interactions under the name of isotopic grand unification. The result was submitted via an apparent resolution of the structural incompatibilities between electroweak and gravitational interactions due to: (1) curvature, because the former are defined on a flat spacetime, while the latter are instead defined on a curved spacetime; (2) antimatter, because the former characterize antimatter via negative-energy solutions, while the latter use instead positive-definite energy-momentum tensors; and (3) basic spacetime symmetries, because the former satisfy the fundamental Poincaré symmetry, which is instead absent for the latter. The main purpose of this paper is to present the methods underlying the isotopic grand unification. We begin with a study of the new mathematics, called isomathematics, and of the related new geometry, called isominkowskian geometry, which permit an apparent resolution of the first incompatibility due to curvature. We then pass to a study of the second novel mathematics, called isodual isomathematics, and related geometry, called isodual isominkowskian geometry, which permit an apparent resolution of the second incompatibility due to antimatter. We then pass to a study of the novel realizations of the conventional Poincaré symmetry, known as Poincaré–Santilli isosymmetry and its isodual, which provide a universal symmetry of gravitation for matter and antimatter, respectively, and permit an apparent resolution of the third incompatibility due to spacetime symmetries. This paper has been made possible by the preceding: memoir5g recently appeared in Rendiconti Circolo Matematico Palermo, which achieves sufficient maturity in the new mathematics; memoir4h recently appeared in Foundations of Physics, which achieves sufficient maturity in the physical realizations of the new mathematics; and memoir8c recently appeared in Mathematical Methods in Applied Sciences, which achieves sufficient maturity in the formulation of the generalized symmetries. Regrettably, in addition to the study of the methods, we cannot study the novel applications and verifications to prevent a prohibitive length. Nevertheless, the reader should be aware that the isominkowskian geometry and its isodual already possess a number of novel applications and experimental verifications in classical physics, particle physics, nuclear physics, astrophysics, gravitation, superconductivity, chemistry, antimatter, and biology, which are indicated in the text with related references without a review.

We present a simple superstring-derived no-scale SUGRA GUT with the D-parity violated SU (4) × SU (2)L × SU (2)R as the gauge symmetry which breaks down to that of MSSM at an intermediate scale M int and further boils down to that of MSM at MS. The massless spectrum at the GUT scale MX consists of three generations of quarks and leptons, Higgs multiplets of [Formula: see text] and some gauge singlet fields (1,1,1)'s. The characteristic features of the model are as follows: (1) The only explicit SUSY breaking parameter is the super-soft (i.e. F-type) scalar mass m of one of [Formula: see text] multiplets, which is generated by the moduli-dominant SUSY breaking source. (2) Both the intermediate and electroweak symmetry breakings respectively at M int ≈ 1011-12 GeV and at ≪ MS are radiatively realized through m for MS ≈ 6 TeV which means [Formula: see text] (effective string unification scale) ≈ 5 × 1017 GeV. (3) The right-handed neutrino with the Majorana mass ≈ M int appears naturally and gives a cosmologically interesting τ-neutrino mass of O(10 eV). (4) The model is quite economical in the sense that each and every member of the Higgs sector has its own function of breaking symmetry and we have no unwanted multiplet.

We consider a particular extension of the scalar two-Higgs potential of the Minimal Supersymmetric Standard Model to an arbitrary number of Higgs doublets. The extended potential has an absolute and only nontrivial minimum that is found exactly. It appears that this minimum is a simple analog to the well-known minimum of the MSSM. This result is applied to a low-energy Higgs potential of the finite Grand Unification Theory where six Higgs doublets are present.

We investigate more generally the possible unification Yang-Mills groups $G_{YM}$ and representations with CP as a gauge symmetry. Besides the possible Yang-Mills groups $E_8$, $E_7$, $SO(2n+1)$, $SO(4n)$, $SP(2n)$, $G_2$ or $F_4$ (or a product of them) which only allow self-contragredient representations, we present other unification groups $G_{YM}$ and representations which may allow CP as a gauge symmetry. These include especially $SU(N)$ containing Weyl fermions and their CP-conjugates from low-energy spectra in a basic irreducible representation (IR). Such an example is the 496-dimensional basic IR (on antisymmetric tensors of rank two) of $SU(32)$ containing $SO(32)$ as a subgroup in the adjoint IR, or $SU(248)$ in a fundamental IR containing $E_8$ as a subgroup in the adjoint IR. Our consideration also leads to the construction of a physical operator (CP) intrincially as an inner automorphism of order higher than two for the unification group. We have also generalized the possible groups as unification $G_{YM}$ to include non-semisimple Lie groups with CP arising as a gauge symmetry. In this case with $U(1)$ ideals in the $G_{YM}$, we found that the $U_Y(1)$ for weak hypercharge in the standard model or a $U(1)$ gauge symmetry at low energies in general is traceless. Possible relevance to superstring theory is also briefly discussed. We expect that our results may open new alternatives for unified model building, especially with deeper or more generalized understanding of anomaly-free theories., Latex, 53 pages, JGTP in press

The present work considers the phase transition between the confinement and "Coulomb" phases in U(1) gauge theory described by Wilson loop action. It was shown (using as an example the approximation of circular loops) that the critical coupling constant is rather independent of the regularization method. Taking into account the renormalization by artefact monopole contributions and the existence of strings in confinement phase assuming the maximal value of the effective fine structure constant equal to α max =π/12≈0.26, we obtain α c ≈0.204, in agreement with Monte Carlo lattice simulation result: α c ≈0.20. Such an approximate regularization independence ("universality") of the critical couplings is needed for the fine structure constant predictions claimed from "the multiple-point criticality principle".

The invention of supersymmetry, almost exactly 25 years ago, changed the face of high-energy physics. The idea that the observed low-energy gauge groups appear due to the process of spontaneous breaking of a single unifying group $G$ is also quite popular. The synthesis of these two elements results in supersymmetric grand unification. I present (perturbatively) exact results regarding the supersymmetric evolution of the gauge couplings from the scale of their unification to lower scales. In particular, it is shown how the heavy mass thresholds can be properly taken into account to all orders., Extended version of the talk at the 4th International Workshop on Supersymmetry and Unification of Fundamental Interactions -- SUSY-96, May 29 -- June 1, University of Maryland, College Park, MD 20742, USA; 25 pages, 2 figures

Texture specific mass matrices generated from the grand unified theory with global family symmetry, have been investigated in the context of latest data regarding [Formula: see text], |Vub|, |Vcb|, |Vtd|, |Vts| and other parameters depending on CKM matrix elements. Unlike several other phenomenological models, the present model not only accommodates the value of [Formula: see text] in the range 150–240 GeV, encompassing the CDF and D0 values, but is also able to reproduce |Vcb| = .038 ± .003 and |Vub/Vcb| = 0.08 ± 0.02, whereas |Vtd| is predicted in the range .005–.014. Further, the angles of the unitarity triangle, related to the CP-violating asymmetries, are in the ranges -1.0 ≤ sin 2α ≤ -.1, .6 ≤ sin 2α ≤ 1.0 and .48 ≤ sin 2β ≤ .56, in agreement with other recent calculations.

The values of αs determined from low and high energy measurements are in irreconcilable contradiction with each other. The current status of the problem is critically reviewed. Consequences of the αs contradiction, in conjunction with other anomalies detected at the Z peak, are discussed. This article has been updated in accordance with experimental numbers reported at summer conferences.

We discuss the problem of building grand unified models in the framework of the dimensional reduction method. In particular, we derive the bosonic sector of the flipped SU(5) grand unified model leading to correct spontaneous symmetry breaking and admitting the hierarchy of masses. For that purpose, we develop a new technique for constructing bases of generators adapted to reductions of representations of Lie algebras to subalgebras.

The structure of the MSSM is reviewed. We first motivate the particle content of the theory by examining the quantum numbers of the known standard model particles and by the requirement of anomaly cancellation. Once the particle content is fixed we can write down the most general renormalizable superpotential. However such a superpotential will contain terms breaking lepton and baryon number which leads us to the concept of R-parity conservation. The question of supersymmetry breaking is discussed next. We list the possible soft breaking terms. However the Lagrangian involving the most general soft breaking terms is phenomenologically intractable because of the appearance of many new parameters. It also leads to some unacceptable predictions. To reduce the number of parameters we restrict ourselves to the case with universal soft breaking terms at the GUT scale. We motivate the need for universal soft breaking terms by the apparent unification of gauge couplings in the MSSM and by the absence of flavor changing neutral currents. Then we discuss radiative electroweak symmetry breaking. Radiative breaking arises because the one-loop corrections involving the large top Yukawa coupling change the sign of the soft breaking mass parameter of the up-type Higgs doublet, this way introducing a nontrivial minimum in the Higgs potential. Finally we give an overview of the possible mixings in the MSSM and enumerate the physical (mass eigenstate) fields together with the mass matrices.

We study the gauge coupling unification of the minimal supersymmetric standard model with non-universal soft scalar and gaugino masses. The unification scale of the gauge couplings is estimated for non-universal cases. It is sensitive to the non-universality. It turns out that these cases can be combined with the assumption of string unification, which leads to a prediction of $\sin^2 \theta_W(M_Z)$ and $k_1$, the normalisation of the $U(1)_Y$ generator. String unification predicts $k_1=1.3 - 1.4$. These values have non-trivial implications on string model building. Two-loop corrections are also calculated. Some of these cases exhibit a large discrepancy between experiment and string unification. We calculate string threshold corrections to explain the discrepancy., Comment: 25 pages, Latex, 4 figures (not included)

We consider heavy nonrelativistic bosons with masses M~MGUT which arise in the Universe during phase transitions with spontaneous symmetry breaking at the grand unification scale. In the frame of statistical mechanics approach with model-independent description of cosmological background we show that the process of emerging of massive GUT bosons looks like evaporation of a Bose condensate. First massive nonrelativistic bosons behave like ideal quantum degenerate Bose gas which has the Gibbons-Hawking temperature due to the presence of the de Sitter event horizon.