Narrow Results

Unifying the massive spin-1 field with gravity requires the implementation of a regular vector field that satisfies the spin-1 Proca equation and is a fundamental part of the space–time metric. That vector field is one of the pair of vectors in the line element field $(X,-X)$, which is paramount to the existence of all Lorentzian metrics and Modified General Relativity (MGR). Symmetrization of the spin-1 Klein–Gordon equation in a curved Lorentzian space–time introduces the Lie derivative of the metric along the flow of one of the regular vectors in the line element field. The Proca equation in curved space–time can then be described geometrically in terms of the line element vector, the Lie derivative of the Lorentzian metric and the Ricci tensor, which unifies gravity and the spin-1 field. Related issues concerning charge conservation and the Lorenz constraint, singularities in a spherically symmetric curved space–time and geometrical implications of MGR to quantum theory are discussed. A geometrical unification of gravity with quantum field theory is presented.

We present a unification algorithm for the λΠ-calculus, the lambda calculus with first-order dependent function types. Our algorithm is an extension of Huet’s algorithm for the simply-typed lambda calculus to first-order dependent function types.

In the simply-typed lambda calculus one attempts to unify a pair of terms of the same type; in the λΠ-calculus types are dependent on terms so one must unify not only terms, but their types as well. Accordingly, we identify a suitable notion of similarity of types, and only attempt to unify a pair of terms of similar type: if the types are not similar then they are not unifiable. Since Huet’s algorithm does not enumerate all of the unifiers of a given pair of terms, the strategy of first unifying pairs of types — by identifying suitable pairs of subterms for unification — is not complete. Accordingly, we must unify terms and their types simultaneously, taking care to maintain all of the conditions that are necessary to ensure the well-formedness of the resulting calculated substitution.

Our notion of substitution is an algebraic one: substitutions are morphisms of λΠ-contexts. However, in order to define our algorithm we must work with psubstitutions and pcontexts — substitutions and contexts, respectively, in which variables are replaced by terms of similar, not β(η)-equal, type.

We carry out an analysis of the non-universal supersymmetry breaking scalar masses arising in SO(10) supersymmetric unification. By considering patterns of squark and slepton masses, we derive a set of sum rules for the sfermion masses which are independent of the manner in which SO(10) breaks to the Standard Model gauge group via its SU(5) subgroups. The phenomenology arising from such non-universality is unaffected by the symmetry breaking pattern, so long as the breaking occurs via any of the SU(5) subgroups of the SO(10) group.

We investigate the requirement of the existence of two degenerate vacua of the effective potential as a function of the Weinberg–Salam Higgs scalar field norm, as suggested by the multiple point principle, in an extension of the Standard Model including seesaw scale physics. Results are presented from an investigation of an extension of the Standard Model to the gauge symmetry group SU(3)_C×SU(2)_L×U(1)′×Ũ(1), where U(1)′ and Ũ(1) originate at the seesaw scale M_SS, when heavy (right-handed) neutrinos appear. The consequent unification of the group SU(3)_C×SU(2)_L×U(1)′ into the flipped SU(5) at the GUT scale leads to the group SU(5)×Ũ(1). We assume the position of the second minimum of the effective potential coincides with the fundamental scale, here taken to be the GUT scale. We solve the renormalization group equations in the one-loop approximation and obtain a top-quark mass of 171±3 GeV and a Higgs mass of 129±4 GeV, in the case when the Yukawa couplings of the neutrinos are less than half that of the top quark at the GUT scale.

The gravitational corrections to the gauge coupling constants of Abelian and non-Abelian gauge theories have been shown to diverge quadratically. Since this result will have interesting consequences, this has been analyzed by several authors from different approaches. We propose to discuss this issue from a phenomenological approach. We analyze the SU(5) gauge coupling unification and argue that the gravitational corrections to gauge coupling constants may not vanish when higher dimensional non-renormalizable terms are included in the problem.

We take the stealth model,¹ an inert multiplet of real scalar singlets, as a candidate for dark matter. We limit the parameter space on the basis of dark matter abundance and direct search experiments. Further we study briefly a real scalar triplet as dark matter candidate. Then a two-component dark matter model is considered, which consists of a real scalar singlet and a scalar triplet with a Z₂×Z₂ symmetry. In a narrow mass range, the direct search experiments start to give some limitations.

Local events are characterized by “where”, “when” and “what”. Just as (bosonic) spacetime forms the backdrop for location and time, (fermionic) property space can serve as the backdrop for the attributes of a system. With such a scenario I shall describe a scheme that is capable of unifying gravitation and the other forces of nature. The generalized metric contains the curvature of spacetime and property separately, with the gauge fields linking the bosonic and fermionic arenas. The super-Ricci scalar can then automatically yield the spacetime Lagrangian of gravitation and the Standard Model (plus a cosmological constant) upon integration over property coordinates.

Sidharth had shown that gravitation can be reconciled with electromagnetic and other forces if we start from a Landau–Ginzburg phase transition. This is further remarked upon and a theory of all forces of nature is proposed.

Considering our (3+1)-dimensional space–time as, in some way, discrete or lattice with a parameter a = λ_P, where λ_P is the Planck length, we have investigated the additional contributions of lattice artifact monopoles to beta functions of the renormalization group equations for the running fine structure constants α_i(μ) (i = 1,2,3 correspond to the U(1), SU(2) and SU(3) gauge groups of the Standard Model) in the Family Replicated Gauge Group Model (FRGGM) which is an extension of the Standard Model at high energies. It was shown that monopoles have N_fam times smaller magnetic charge in FRGGM than in SM (N_fam is the number of families in FRGGM). We have estimated also the enlargement of a number of fermions in FRGGM leading to the suppression of the asymptotic freedom in the non-Abelian theory. We have shown that, in contrast to the case of anti-GUT when the FRGGM undergoes the breakdown at μ = μ_G ~ 10¹⁸GeV, we have the possibility of unification if the FRGGM-breakdown occurs at μ_G ~ 10¹⁴GeV. By numerical calculations we obtained an example of the unification of all gauge interactions (including gravity) at the scale μ_GUT ≈ 10^18.4GeV. We discussed the possibility of [SU(5)]³ or [SO(10)]³ (SUSY or not SUSY) unifications.

We provide a conceptual unified description of the quantum properties of black holes (BH), elementary particles, de Sitter (dS) and Anti-de Sitter (AdS) string states.The conducting line of argument is the classical–quantum (de Broglie, Compton) duality here extended to the quantum gravity (string) regime (wave–particle–string duality). The semiclassical (QFT) and quantum (string) gravity regimes are respectively characterized and related: sizes, masses, accelerations and temperatures. The Hawking temperature, elementary particle and string temperatures are shown to be the same concept in different energy regimes and turn out the precise classical–quantum duals of each other; similarly, this result holds for the BH decay rate, heavy particle and string decay rates; BH evaporation ends as quantum string decay into pure (nonmixed) radiation. Microscopic density of states and entropies in the two (semiclassical and quantum) gravity regimes are derived and related, an unifying formula for BH, dS and AdS states is provided in the two regimes. A string phase transition towards the dS string temperature (which is shown to be the precise quantum dual of the semiclassical (Hawking–Gibbons) dS temperature) is found and characterized; such phase transition does not occurs in AdS alone. High string masses (temperatures) show a further (square root temperature behavior) sector in AdS. From the string mass spectrum and string density of states in curved backgrounds, quantum properties of the backgrounds themselves are extracted and the quantum mass spectrum of BH, dS and AdS radii obtained.

The Extended Supersymmetric Standard Model (ESSM), motivated on several grounds, introduces two vectorlike families [ of SO(10)] with masses of order 1 TeV. In an earlier work, a successful pattern for fermion masses and mixings (to be called pattern I) has been proposed within a unified SO(10)-framework, based on MSSM, which makes seven predictions, in good accord with observations, including V_cb ≈ 0.04, and sin² 2θ_νμντ ≈ 1. Extension of this framework to ESSM, preserving the successes of pattern I, has recently been proposed, where it was noted that ESSM can provide a simple explanation of a possible anomaly in (g-2)_μ. To exhibit new phenomenological possibilities which may arise within ESSM, we present here a variant pattern (to be called pattern II) for fermion masses and mixings, within the SO(10)/ESSM framework, which possesses the same degree of success as pattern I as regards the masses and mixings of all fermions including neutrinos. We first note that either one of these two patterns, embedded in ESSM, would lead to a reduction in the LEP neutrino-counting from N_ν = 3 (in good agreement with the data) and also provide a simple explanation of a possible (g-2)_μ-anomaly. They can, however, be distinguished from each other by (a) a sharpening of our understanding of the true magnitude of the anomaly in ν_μ-nucleon scattering recently reported by the NuTeV group, (b) improved measurements of m_t, m_H and m_W, (c) improved tests of e–μ lepton-universality in charged current processes, and (d) improvements in the measurements of V_ud and V_us. Both patterns would predict some departure from the SM as regards tau lifetime. The probes listed above, and, of course, direct searches for the vectorlike families at the LHC and a future NLC can clearly test ESSM, and even distinguish between certain variants.

This paper is composed of two correlated topics: (1) unification of gravitation with gauge fields; (2) the coupling between the daor field and other fields and the origin of dark energy. After introducing the concept of "daor field" and discussing the daor geometry, we indicate that the complex daor field has two kinds of symmetry transformations. Hence the gravitation and SU(1, 3) gauge field are unified under the framework of the complex connection. We propose a first-order nonlinear coupling equation of the daor field, which includes the coupling between the daor field and SU(1, 3) gauge field and the coupling between the daor field and the curvature, and from which Einstein's gravitational equation can be deduced. The cosmological observations imply that dark energy cannot be zero, and which will dominate the doom of our Universe. The real part of the daor field self-coupling equation can be regarded as Einstein's equation endowed with the cosmological constant. It shows that dark energy originates from the self-coupling of the space–time curvature, and the energy–momentum tensor is proportional to the square of coupling constant λ. The dark energy density given by our scenario is in agreement with astronomical observations. Furthermore, the Newtonian gravitational constant G and the coupling constant ∊ of gauge field satisfy G = λ²∊².

A theory in which four-dimensional space–time is generalized to a larger space, namely a 16-dimensional Clifford space (C-space) is investigated. Curved Clifford space can provide a realization of Kaluza–Klein. A covariant Dirac equation in curved C-space is explored. The generalized Dirac field is assumed to be a polyvector-valued object (a Clifford number) which can be written as a superposition of four independent spinors, each spanning a different left ideal of Clifford algebra. The general transformations of a polyvector can act from the left and/or from the right, and form a large gauge group which may contain the group U(1) × SU(2) × SU(3) of the standard model. The generalized spin connection in C-space has the properties of Yang–Mills gauge fields. It contains the ordinary spin connection related to gravity (with torsion), and extra parts describing additional interactions, including those described by the antisymmetric Kalb–Ramond fields.

We elaborate that general intersecting brane models on orbifolds are obtained from type I string compactifications and their T-duals. Symmetry breaking and restoration occur via recombination and parallel separation of branes, preserving supersymmetry. The Ramond–Ramond tadpole cancellation and the toron quantization constrain the spectrum as a branching of the adjoints of SO(32), up to orbifold projections. Since the recombination changes the gauge coupling, the single gauge coupling of type I could give rise to different coupling below the unification scale. This is due to the nonlocal properties of the Dirac–Born–Infeld action. The desirable weak mixing angle sin²θ_W = 3/8 is naturally explained by embedding the quantum numbers to those of SO(10).

In the present paper we develop a concept of parallel ordinary (O) and mirror (M) worlds. We have shown that in the case of a broken mirror parity (MP), the evolutions of fine structure constants in the O- and M-worlds are not identical. It is assumed that E₆-unification inspired by superstring theory restores the broken MP at the scale ~ 10¹⁸GeV, what unavoidably leads to the different E₆-breakdowns at this scale: E₆ → SO(10) × U(1)_Z — in the O-world, and E′₆ → SU(6)′ × SU(2)′_Z — in the M-world. Considering only asymptotically free theories, we have presented the running of all the inverse gauge constants in the one-loop approximation. Then a "quintessence" scenario suggested in Refs. 56–61 is discussed for our model of accelerating universe. Such a scenario is related with an axion ("acceleron") of a new gauge group SU(2)′_Z which has a coupling constant g_Z extremely growing at the scale Λ_Z ~ 10^-3eV.

In this paper, we construct a model based on a flipped SU(5) partial grand unified theory, within the framework of the Randall–Sundrum (RS1) proposal. Breaking of is achieved using a bulk scalar field in the 10 of SU(5), Φ, which gains a vacuum expectation value <Φ> ~ 3 × 10¹⁵GeV. We are able to retain the successes of the phenomenology, specifically the confinement of all fields to the smallest (1, , and 10) representations of SU(5). We derive the beta functions, and point out some constraints on bulk matter content implied by the runnings (and positivity) of the five-dimensional coupling. Finally, we comment on baryon decay and show the fine-tuning problem required to prevent an exponentially short proton lifetime.

We study various possible Supersymmetric Left–Right (SUSYLR) models with Higgs doublets carrying B-L charge ±1: with single step symmetry breaking down to the Minimal Supersymmetric Standard Model (MSSM) as well as multistep symmetry breaking. Single step symmetry breaking can be achieved with the minimal field content of just Higgs doublet and bidoublets whereas multistep symmetry breaking can be realized only at the cost of including additional Higgs superfields. However, going beyond the minimal field content comes up with the exciting possibility of TeV scale intermediate symmetry which can have important implications in the ongoing collider experiments. We show that spontaneous parity violation can be achieved naturally in all these models and R-parity is spontaneously broken by the vacuum expectation value of B-L odd Higgs doublets. The tiny neutrino mass can arise from a double seesaw mechanism in the presence of additional singlet or triplet fermions. We show that gauge coupling unification can be achieved in these models with the possibility of TeV scale intermediate symmetry in some specific nonminimal versions.

A brief overview of Higgs physics and of supersymmetry is given. The central theme of the overview is to explore the implications of the recent discovery of a Higgs-like particle regarding the prospects for the discovery of supersymmetry assuming that it is indeed the spin-0 CP even boson that enters in the spontaneous breaking of the electroweak symmetry. The high mass of the Higgs-like boson at ~125 GeV points to the weak scale of supersymmetry that enters in the loop correction to the Higgs boson mass, to be relatively high, i.e. in the TeV region. However, since more than one independent mass scales enter in softly broken supersymmetry, the allowed parameter space of supersymmetric models can allow a small Higgs mixing parameter μ and light gaugino masses consistent with a ~125 GeV Higgs boson mass. Additionally some light third generation sfermions, i.e. the stop and the stau are also permissible. Profile likelihood analysis of a class of SUGRA models indicates that m_A>300 GeV which implies one is in the decoupling phase and the Higgs couplings are close to the standard model in this limit. Thus a sensitive measurement of the Higgs couplings with fermions and with the vector bosons is needed to detect beyond the standard model effects. Other topics discussed include dark matter, proton stability, and the Stueckelberg extended models as probes of new physics. A brief discussion of the way forward in the post Higgs discovery era is given.

We consider a graviweak unification model with the assumption of the existence of a hidden (invisible) sector of our Universe, parallel to the visible world. This Hidden World (HW) is assumed to be a Mirror World (MW) with broken mirror parity. We start with a diffeomorphism invariant theory of a gauge field valued in a Lie algebra , which is broken spontaneously to the direct sum of the space–time Lorentz algebra and the Yang–Mills algebra: — in the ordinary world, and — in the hidden world. Using an extension of the Plebanski action for general relativity, we recover the actions for gravity, SU(2) Yang–Mills and Higgs fields in both (visible and invisible) sectors of the Universe, and also the total action. After symmetry breaking, all physical constants, including the Newton's constants, cosmological constants, Yang–Mills couplings, and other parameters, are determined by a single parameter g present in the initial action, and by the Higgs VEVs. The dark energy problem of this model predicts a too large supersymmetric breaking scale (M_SUSY ~10¹⁰GeV), which is not within the reach of the LHC experiments.

We develop the general relativity of extended spacetime–property for describing events including their properties. The anticommuting nature of property coordinates, augmenting spacetime (x, t), allows for the natural emergence of generations and for the simple incorporation of gauge fields in the spacetime–property sector. With one electric property, this results in a geometrical unification of gravity and electromagnetism, leading to a Maxwell–Einstein Lagrangian plus a cosmological term. Addition of one neutrinic and three chromic properties should lead to unification of gravity with electroweak and strong interactions.