Gauge hierarchies of SU(N) grand unification

The structure of spontaneous breaking of SU(N) gauge symmetry for grand unification is investigated. The results obtained are applied to the analysis of SU(8) symmetry for which possible ways of breaking and intermediate symmetries are considered. It is assumed that the SU(8) group unifies the subgroups of colour, standard electroweak and horizontal symmetries. We find conditions which it is necessary to impose on the vacuum expectation values of Higgs multiplets to provide an arbitrary breaking pattern of SU(N) symmetry and conserve any intermediate symmetry. If in the SU(8) models considered fermions and mirror fermions do not violate the (V-A) and (V+A) structure of weak interactions, then their masses should not be greater than ～10² GeV. It is also shown that the contributions of fermion and Higgs multiplets to the renormalization group equation for the coupling constant of any subgroup of SU(N) are identical. Renormalization group identities for the case of arbitrary SU(N) breaking are given where the contribution of Higgs multiplets have been taken into account (but they cancel each other). Using these identities one can calculate the mass values for the breaking of the intermediate symmetries in the SU(8) models, and also exclude part of the possible breaking patterns.     

Hypothesis of friedmons as dark matter particles

The hypothesis of friedmons, the particles of mass 1.53 · 10^?15 g, as candidates to dark matter particles is presented. Friedmons are stable bicolor lepton structures corresponding to exact symmetry group SU(2), the dual group of electroweak interaction. Similarly to the fact that the nucleon mass is related to the average star mass, the friedmon mass is related to the mass of the Metagalaxy whose metric is close to the de Sitter metric and which can be qualitatively considered as a white hole with an event horizon defined by the cosmological constant.     

宇宙创生于真空涨落的一个可能方案——原初暴涨宇宙模型

大爆炸宇宙模型的成功说明宇宙有可能是创生出来的。宇宙究竟是创生于“无”,还是创生于真空涨落?这是目前正在热烈讨论的问题。本文提出宇宙创生于真空涨落的一种可能的方案。我们提出,在单圈近似下的真空涨落创生了原初暴涨宇宙—原初deSitter宇宙,这时SO₁₁,SU₁₄或E₈×E₈对称性成立。由于规范耦合常数g和Higgs场自耦合常数λ的渐近自由,将使得原初大统一破缺发生一级相变,相变时释放出的潜热化为宇宙的原初物质,以使宇宙升温到接近Planck温度。这样所创生的宇宙即由原初暴涨阶段过渡到以辐射为主的标准模型。此后,例如SU₅GUT成立,在创生后的10^-35秒,将发生熟知的第二次暴涨。 关键词：     

Radiative gauge symmetry breaking in supersymmetric flipped SU(5)

The radiative breaking of the SU(5)×U(1) symmetry in the flipped SU(5) model recently proposed by Antoniadis et al. is studied using renormalization group techniques. It is shown that gaugino masses can only be the dominant source of supersymmetry breaking at the Planck scale if the U(1) gaugino mass M₁ is at least 10 times larger than the SU(5) gaugino mass M₅. If M₁≅M₅ at the Planck scale, non-vanishing trilinear soft breaking terms (“A-terms”) are needed already at the Planck scale. In both cases consequences for the sparticle spectrum at the weak scale are discussed.     

Departures from chiral symmetry

We review the physical concepts supporting the notion of an approximate hadron symmetry with special emphasis on the Nambu-Goldstone realizations of chiral SU (2) × SU (2) and SU (3) × SU (3). We stress the role of perturbation theory in the symmetry breaking as the technical instrument to connect broken symmetries with experiment. This is an alternate to the treatments that stress PCAC and current algebra. We find that chiral SU (2) × SU (2) is a good hadron symmetry to within 7% making it the best hadron symmetry after isotopic symmetry. The nonrenormalization theorem, Σ-terms, K_l3 decay, η→3π decay, the Goldberger-Treiman relation and many other specific processes and their relation to approximate chiral symmetry are discussed.     

Left-right symmetry breaking scale and supersymmetry in unified theories

We propose a class of supersymmetric grand unified models where parity and SU(2)_R breaking scales are widely separated and compatible with a low-lying mass for the right-handed gauge boson W_R. The intermediate symmetry SU(4)_c×SU(2)_L×SU(2)_R and Higgs content are uniquely fixed if m_WR < 10⁹ GeV. The unification scale lies within an order of magnitude below the Planck mass.     

Strong spin-two interaction and general relativity

The concept of short range strong spin-two (f) field (mediated by massive f-mesons) and interacting directly with hadrons was introduced along with the infinite range (g) field in early seventies. In the present review of this growing area (often referred to as strong gravity) we give a general relativistic treatment in terms of Einstein-type (non-abelian gauge) field equations with a coupling constant G_f ? 10³⁸G_N (G_N being the Newtonian constant) and a cosmological term λ_f ?;_μν (?;_μν is strong gravity metric and λ_f ～ 10²⁸ cm^? is related to the f-meson mass). The solutions of field equations linearized over de Sitter (uniformly curves) background are capable of having connections with internal symmetries of hadrons and yielding mass formulae of SU(3) or SU(6) type. The hadrons emerge as de Sitter “microuniverses” intensely curved within (radius of curvature ～10^?14 cm).The study of spinor fields in the context of strong gravity has led to Heisenberg's non-linear spinor equation with a fundamental length ～2 × 10^?14 cm. Furthermore, one finds repulsive spin-spin interaction when two identical spin-$\text{1}\text{2}$ particles are in parallel configuration and a connection between weak interaction and strong gravity.Various other consequences of strong gravity embrace black hole (solitonic) solutions representing hadronic bags with possible quark confinement, Regge-like relations between spins and masses, connection with monopoles and dyons, quantum geons and friedmons, hadronic temperature, prevention of gravitational singularities, providing a physical basis for Dirac's two metric and large numbers hypothesis and projected unification with other basic interactions through extended supergravity.     

Can the superstring inspire the standard model?

We discuss general features of models in which the E₈ × E′₈ heterotic superstring is compactified on a specific Calabi-Yau manifold. The gauge group of rank-6 in four dimensions is supposed to be broken down at an intermediate scale m_I to the standard model group SU(3)_C × SU(2)_L × U(1)_Y, as a result of two neutral scalar fields acquiring large vacuum expectations (vev's) in one of many flat directions of the effective potential. We find that it is difficult to generate such an intermediate scale by radiative symmetry breaking, whilst such models have prima facie problems with baryon decay mediated by massive particles and with non-perturbative behaviour of the gauge couplings, unless m_I ≳ 10¹⁶ GeV. Rapid baryon decay mediated by light particles, large neutrino masses, other Δ L ≠ 0 processes and flavour-changing neutral currents are generic features of these models. We illustrate these observations with explicit calculations in a number of different models given by vev's in different flat directions.     

Symmetrieeigenschaften achtkomponentiger Spinorfelder im Gitterraum

Starting from the four component Dirac equation for free particles without mass W.Heisenberg und W.Pauli have shown that the interaction term is uniquely defined, if one requires that all symmetries of free particles are preserved. Here we obtain similar results if we start from the eight component Dirac equation for free particles without mass:

1. The symmetry group of the eight component Dirac equation for free particles without mass has 16 parameters. It is isomorph to the direct product of the SU 4 and a one-parametric group: SU 4× (1).
2. The interaction operator is uniquely defined if one requires to preserve as many symmetries as possible of those given in (1).
3. But some of the symmetries in (1) are necessarily broken, in particular that of SU 3. The symmetry of the interaction operator is given by SO 4× (1)× (1).

These results mean:

1. The Heisenberg theory is uniquely defined, only if one assumes that the free particle part of the equation is well known.
2. The theory can be changed without modifying the fundamental idea ofHeisenberg andPauli to deduce an uniquely defined interaction operator if one starts with a modified free particle part.
3. A special kind of modification of the free particle part leads essentially to the SU 4-symmetry including that of SU 3, which is necessarily broken by the interaction term.
4. The question arises if this break of the SU 3-symmetry has something to do with the real break. This question is not yet touched in this paper.

     

Prospects for superstring models with two vacuum expectation values for standard model singlets

The spontaneous breaking of rank-six intermediate groups to the standard model in superstring phenomenology is examined. It requires the existence of two vacuum expectation values, one for each standard model singlet in the 27 chiral representation of E₆. We use a simplified model based on the group SU(3)_c×SU(2)_L×SU(2)_R×U(1)_L×U(1)_R. It is found that the well-known phenomenological constraints such as proton decay, vanishing neutrino masses and flavour-changing neutral currents allow for the possibility of sizeable Yukawa couplings for the two standard model singlets which can originate low energy negative masses. The proof of this radiative breaking relies, however, on several parameters whose magnitude is unpredicted, but is facilitated if the mass of the exotic quark is large (∼300 GeV).     

Types of two-dimensionalN = 4 superconformal field theories

Various types ofN = 4 superconformal symmetries in two dimensions are considered. It is proposed that apart from the well-known cases ofSU (2)and SU(2) × SU(2) ×U (1), their Kac-Moody symmetry can also be SU(2) × (U (1))⁴. Operator product expansions for the last case are derived. A complete free field realization for the same is obtained     

Composite symmetries and sub-constituent models

Assuming the internal A-spin, B-spin and C-spin of particles from basic symmetry SO(4), the color SU(3), horizontal SU(3)', electroweak SU(2)'_w×U(1) and other higher composite symmetries are derived.     

Fermion masses in grand unified theories: Effective Yukawa terms

It is argued that effective non-renormalizable terms of the type recently proposed by Ellis and Gaillard can give rise to large contributions to the fermion masses. The combined effect of this kind of term and the usual Yukawa couplings could explain the observed hierarchy of fermion masses. Two toy-models based on the gauge groups SU (5)×SU(2) _H and SO(10)×SU(2) _H (where SU(2) _H is a gauged “horizontal” symmetry) are shown in which one can obtain some interesting mass relations previously obtained under very different assumptions.     

Left-right symmetric theories and vacuum domain walls and strings

Theories in which a discrete left-right symmetry is spontaneously broken are expected to lead to the formation of vacuum domain walls. Although the existence of such walls at the present epoch is observationally excluded, we show that such theories are allowed if the discrete symmetry is embedded in a larger continuous symmetry, e.g., SO(10), spontaneously broken at higher temperatures. In this case vacuum strings are formed when the larger symmetry is broken, and these become connected by domain walls when the discrete symmetry is broken. The bounded domain walls tend to shrink, and the system of strings and domain walls decays before its energy density becomes comparable to that of matter. In particular, our arguments allow the symmetry breaking pattern SO(10) → … S[O(6)×O(4)] → SU(3)×SU(2)×U(1) which has been proposed by others.     

Virtual effects of Higgs particles

The possibility of observing Higgs particles through virtual effects is considered in detail for a general gauge theory. The effect of charged Higgs particles on low-energy weak interaction processes, like muon decay, tau decay, nuclear beta decay, pion decay, and some higher-order processes is analyzed. The effect of flavor-changing neutral Higgs particles on rare decay modes of the muon and kaon, μe conversion, K^o-$\text{K}$^o and D^o-$\text{D}$^o mixing is also studied. We discuss constraints on possible extensions of the Weinberg-Salam model and experiments sensitive to their Higgs particles. In particular, we analyze the neutral Higgs which couple to fermions in the minimal SU(2)_L×SU(2)_R×U(1) model and find that they probably have mass greater than 100 GeV.     

Chiral symmetry breaking and condensates in the rishon model

The rishon model is studied in the limit g_c → 0, α → 0 when its global flavour symmetry is SU(6) × SU(6) × U(1) analogous to six massless flavour QCD. Recently it was shown that the ad hoc breaking SU(6) × SU(6) → SU(3) × SU(3) allows the anomaly constraint to be satisfied. In this paper this is shown to be but one of several successful patterns of chiral symmetry breaking. The condensates required to perform these breakings are fully discussed. A plausibility argument based on single gauge boson exchange is presented which determines the condensate uniquely to be 〈(v_LV_L)³〉 corresponding to the original breaking above. The same argument applies to QCD, which is argued to differ in its chiral behaviour due to the large intrinsic masses of the quarks. The implications of the above condensate and pattern of chiral symmetry breaking for the rishon model include the prediction of integer charged colour octet fermions, a naive mass formula m_e = 2m_u ? m_d, new insight into the parity-violating condensate 〈(v_Lv_L)²(v_Rv_R)〉 and the prediction of 52 new pseudos whose masses are estimated.     

Aspects of the super-unification of strong,electroweak and gravitational interactions

We develop a strategy for extracting low-energy phenomenological four-dimensional physics from the superstring. We discuss supersymmetry and gauge symmetry breaking, emphasizing key ingredients in the construction of a realistic model based on Calabi-Yau compactification. The incorporation of a no-scale mechanism for the dynamical generation of the electroweak gauge hierarchy imposes a unique choice of the gauge group SU(3) × SU(2) × U(1)², an almost unique set of matter fields and of Yukawa couplings. Our phenomenological analysis of this model includes the derivation of bounds on the mass of the new neutral gauge boson from the Z⁰ boson mass, low-energy neutral currents, and cosmology. We calculate the ratios of sparticle masses and give estimates of their magnitudes. These are based on detailed dynamical calculations demonstrating the feasibility of weak gauge symmetry breaking, made possible by radiative corrections to supersymmetry breaking initiated by a gaugino mass.     

Models of non-abelian orbifolds

Several models of non-abelian orbifolds have been constructed. There are models with three or four families of quarks and leptons, and gauge symmetry SU(3) × SU(2) × SU(2) × U(1)² × SU(3)′ × SO(10)′ × U(1)′ or SU(3) × SU(2) × U(1)³ × SU(4)′ × SO(8)′ × U(1)′.     

The Planck Aether model for a unified theory of elementary particles

A dense assembly of an equal number of two kinds of Planck masses, one having positive and the other one negative kinetic energy, described by a nonrelativistic nonlinear Heisenberg equation with pointlike interactions, is proposed as a model for a unified theory of elementary particles. The dense assembly of Planck masses leads to a vortex field below the Planck scale having the form of a vortex lattice, which can propagate two types of waves, one having the property of Maxwell's electromagnetic and the other one the property of Einstein's gravitational waves. The waves have a cutoff at a wavelength equal to the vortex lattice constant about 10³ times larger than the Planck length, reproducing the GUT scale of elementary particle physics. The vortex lattice has a resonance energy leading to two kinds of quasiparticles, both of which have the property of Dirac spinors. Depending on the resonance energy, estimated to be 10⁷ times smaller than the Planck energy, the mass of one of these quasiparticles is about equal to the electron mass. The mass of the other particle is much smaller, making it a likely candidate for the much smaller neutrino mass. Larger spinor masses occur as internal excitations, with a maximum of four such excitations corresponding to a maximum of four particle families. Other vortex solutions may describe the quark-lepton symmetries of the standard model. All masses, with the exception of the Planck mass particles, are quasiparticles for which Lorentz invariance holds, with the Galilei invariance at the Planck scale dynamically broken into Lorentz invariance below this scale. The assumed equal number of Planck masses with positive and negative kinetic energy makes the cosmological constant exactly equal to zero.     

Light quarks mass effect on the color ferromagnet model of the QCD vacuum

We study the effect of quark masses on the energy density of two ferro-magnetic vacua in QCD, corresponding to different vacuum symmetries. In the massless limit the two states have the same energy, while as the quark masses are turned on the state with more symmetry elements becomes the “true” vacuum. The dominant contribution to the energy density splitting is proportional tom ² lnm ²