Phase portrait ofSU(5) model. II intermediate phasesSU(3)×[U(1)]2 and [SU(2)]2×[U(1)]2

The effective potential of the scalar field in theSU(5) model has extrema with symmetry:SU(5),SU(4)×U(1),SU(3)×SU(2)×U(1),SU(3)×[U(1)]², [SU(2)]²×[U(1)]². In our recent paper it was shown that theSU(4)×U(1) phase as well asSU(3)×SU(2)×U(1) phase were stable at the nonzero temperature in a vast region of parameters. In the present paper it is found that the [SU(2)]²×[U(1)]² symmetric vacuum is unstable and theSU(3)×[U(1)]² symmetric vacuum can be metastable in the certain interval of the temperature. Domains of the three phases:SU(4)×U(1),SU(3)×SU(2)×U(1),SU(3)×[U(1)]²-could co-exist in the early. Universe.     

A low composite scale preon model with complementarity

We have constructed the first “realistic candidate” preon model with low composite scale satisfying complementarity between the Higgs and confining phases. The model is based onSU(4) metacolor and predicts four generations of ordinary quarks and leptons together with heavy neutrinos at the level of the standard gauge groupSU(3) _c ×SU(2) _L ×U(1) _Y . There are no exotic massless fermions. The global family group isSU(2)×U(1).     

A toy model for Hidden Weinberg-Salam Higgs particle

We show that in theSU(2)×U(1) model with one more Higgs singlet, the Weinberg-Salam Higgs can be made Hidden.     

Supersymmetric models of weak and electromagnetic interactions

General method of spontaneous supersymmetry breaking is developed. On its basis a number of unified lepton models is analyzed. Examples of realistic lepton models based on the groups SU(2) × U(1) and SU(2) × SU(2) × U(1) are considered.     

TheY(Y L ), a compositeness-inspired extra gauge boson

We show that the (isoscalar)Y(Y _L ) boson, originally introduced on the basis of compositeness andW, Y(Y _L ) dominance can be understood as an extra gauge boson within aU(1) _B ×SU(2) _L ×U(1) _Y gauge theory broken by an appropriate choice of the Higgs sector. Radiative-correction effects can thus be calculated as reliably as in theSU(2) _L ×U(1) _Y , theory when comparing the predictions with forthcoming precision data in theSLC/LEP energy range.     

Quaternionic-valued Gravitation in 8D, Grand Unification and Finsler Geometry

A unification model of 4D gravity and SU(3)×SU(2)×U(1) Yang-Mills theory is presented. It is obtained from a Kaluza-Klein compactification of 8D quaternionic gravity on an internal CP ²=SU(3)/U(2) symmetric space. We proceed to explore the nonlinear connection formalism used in Finsler geometry to show how ordinary gravity in D=4+2 dimensions has enough degrees of freedom to encode a 4D gravitational and SU(5) Yang-Mills theory. This occurs when the internal two-dim space is a sphere S ². This is an appealing result because SU(5) is one of the candidate GUT groups. We conclude by discussing how the nonlinear connection formalism of Finsler geometry provides an infinite hierarchical extension of the Standard Model within a six dimensional gravitational theory due to the embedding of SU(3)×SU(2)×U(1)⊂SU(5)⊂SU(∞).     

Projective spacetime

It is suggested that the world is locally projectively flat rather than Euclidean. From this postulate it is shown that an (N+1)-particle system has the global geometry of the symmetric spaceSO(4,N+1)/SO(4)×SO(N+1). A complex representation also exists, with structureSU(2,N+1)/S[U(2)×U(N+1)]. Several aspects of these geometrics are developed. Physical states are taken to be eigenfunctions of the Laplace-Beltrami operators. The theory may provide a rational basis for comprehending the groupsSO(4, 2),SU(2)×U(1),SU(3), etc., of current interest.     

The symmetry breaking patternSU(5)→SU(3)×U(1) including one loop radiative corrections

We derive conditions on the Higgs parameters of the minimalSU(5) model under which the phenomenologically desired symmetry breaking patternSU(5)→SU(3)×U(1) persists at the one loop level.     

A supersymmetricSU(5)×U(1) model with natural gauge hierarchy

We present a supersymmetricSU(5)×U(1) model. This model has the following features. The gauge hierarchy is naturally generated by the quadratically divergent nature of the Fayet-IliopoulosD term. TheSU(5)×U(1) gauge symmetry breaks uniquely intoSU(3) _W ×SU(2) _c ×U(1) _y at an energy scale of 10^17–18GeV. The non-vanishing vacuum expectation value of an auxiliary field component ofU(1) gauge vector multiplet induces the breaking ofSU(2) _W ×U(1) _y . It gives a mass of 10^2–3GeV to scalar quarks and scalar leptons at the tree level. The renormalization group analysis shows that the color fine structure constant α _C (M _W ) becomes somewhat small and the Weinberg angle sin²θ _W (M _W ) somewhat too large in a simple version of the model.     

Construction of grand unified models under maximal subalgebras

A construction of grand unified models of the strong, weak and electromagnetic interactions is described based on the transformation properties of the group generators under a maximal subgroup decomposition without recourse to large representation matrices or to the specific algebraic structures of some classical Lie-groups, such as the Clifford algebra associated with the orthogonal groups or the octonionic structure of the exceptional groups. To illustrate the procedure an explicit construction is given of the SU(5) model useful in the discussion of higher rank groups, of SO(10) under the maximal subalgebras SU(2)_L × SU(2)_R × SU(4)_c and SU(5) × U(1)_r and of the exceptional group E₆ under SU(3)_L × SU(3)_R × SU(3)_c and SO(10) × U(1)_t. The construction procedure can be used as well with any classical Lie-group.     

The construction of vector-like supersymmetric gauge models of weak and electromagnetic interactions

Despite great efforts and partial successes the situation with respect to spontaneously broken supersymmetric unified gauge models of weak, electromagnetic and strong interactions has remained quite unsatisfactory up to now. Starting from the most simple SU(2) × U(1) cases we exploit possible extensions. This naturally leads to a consideration of vector-like models with—in the first instance—a larger number of multiplets. Although the later can be made massive without spoiling the conservation of fermion number, the additional massive fermions only show parity conserving interactions with all the intermediate vector fields. Therefore models with larger gauge groups are considered: SU(2) × SU(2) × U(1) with two quartets, SU(3) × U(1) with four triplets, and finally SU(3) × SU(2) × U(1) with two sextets of matter fields. None of these can be accepted yet as a true model for physical particles, but it is shown how different negative features in the simple theories may be avoided in the more complicated ones. Thus our results may be considered as an encouraging starting point for investigations of larger gauge groups in supersymmetric models.     

Supersymmetric non-linear σ model onE 8/SO(10)×SU(3)×U(1)

We calculate the Kähler potential of theE ₈/SO(10)×SU(3)×U(1) homogeneous space. Some quasi Nambu-Goldstone fermions living in the corresponding supersymmetric non-linear σ model are identified with the usual three families of quarks and leptons, and one mirror family. We also show that the dynamical breakdown of supersymmetry does not occur in this model.     

Baryon number non-conservation as a low-scale phenomenon

We analyse Baryon number non-conservation as a result of scalar boson mediated interactions characterised by a low mass scale (in the TeV region) in the framework of the standardSU(3)×SU(2)×U(1) gauge group.     

Nonabelian electric and magnetic flux in unified SU(5) gauge theory

We study the long-distance behaviour of pure unified SU(5) gauge theory in the limit when the electroweak subgroup is unbroken. We show that the symmetry breaking pattern SU(5)→SU(3)_c×SU(2)×U(1)_Y, with SU(3)_c and SU(2) ×U(1)_Y realized, respectively, in confining and coulombic phases, is a possible dynamical phase of the SU(5) theory. The proof relies on showing that the duality equation of 't Hooft, relating the electric and magnetic flux, is exactly satisfied for the above symmetry breaking pattern. The infrared structure of SU(5), broken down to SU(3)_c×SU(2)×U(1)_Y, is not self-dual.     

Aspects of left-right symmetric models in superstring phenomenology

The general features of low-energy, rank-six left-right symmetric models as inspired by the superstring are examined. Particular attention is paid to the mass-mixing matrix of the exotic and downtype quarks. It is found that the class of models based on the groupSU(3) _C ×SU(2) _L ×SU(2) _N ×U(1) _L ×U(1) _R is plagued with the problem of unnatural fine tuning. Models based on the other left-right group, namelySU(3) _C ×SU(2) _L ×SU(2) _N ×U(1) _L ×U(1) _R , work rather well from the points of view investigated. In this case a parameter fitting is presented which is compatible with the lowering of the group rank by two units via radiative breaking, without conflicting either with weak universality or with lepton conservation. The unification scale comes in the 10¹⁷ GeV mass range, the intermediate (righthanded) scale is quite low, not exceeding the 10⁴ GeV range, and the Weinberg angle is correct. Good prospects are also obtained for proton decay and neutrino masses.     

B^0 - \bar B^0 mixing in a supersymmetric model without at-quark

A model based on a low energySU(3)_c×SU(2)₁×SU(2)₂×U(1) _H gauge group is considered. Theb-quark couples mainly to thec-quark via a new heavyW-boson and thet-quark is omitted altogether. The model is shown to be compatible with low energy charged current data. \(B_d^0 - \bar B_d^0 \) mixing occurs through the exchange of the heavyW-boson and through gluino exchange in the supersymmetric version of the model. The calculated mixing is much smaller in both cases than the observed effect and the model is, therefore, ruled out.     

Algebraic constraints for higgs multiplets

The phenomenon of spontaneous breaking of a gauge symmetry group, provides a number of algebraic constraints which Scalar Higgs mesons have to satisfy. We discuss these constraints and give details for the cases ofSU(2),SU(2) ×U(1) andSU(3).     

Radiative quark masses constrained by the gauge group only

We discuss the possibility of obtaining the observed pattern of quark masses and mixings as a consequence of radiative corrections, gauge invariance and particle content of the theory. We do not allow any kind of additional symmetry, such as family and discrete symmetries. A model based on the gauge groupSU(3)×SU(2) _L ×SU(2) _R ×U(1) _B?L is considered. It turns out that the correct values of quark masses can be reasonably reproduced. The typical strength of the flavour changing couplings of theZ ⁰-boson is however at least one order of magnitude above the experimental upper bounds. A comparison is made with a model in which an additional discrete symmetry is present. In this case flavour changing phenomena can be kept under control.     

Natural flavour conservation in the neutral currents and the determination of the Cabibbo angle

We point out a conflict between the requirement of natural flavour conservation in the neutral currents and the possibility of determining the generalized Cabibbo angles as a function of the quark masses in the SU(2) × U(1) and in the SU(2)_L × SU (2)_R × U (1) models. The general implications of natural flavour conservation in the neutral currents on the fermion mass matrices are also discussed.     

The standard model from a gauge theory in ten dimensions via CSDR

We present a gauge theory in ten dimensions based on the gauge group E₈ which is dimensionally reduced, according to the coset space dimensional reduction (CSDR) scheme, to the standard model SU_3c×SU_2L×U₁, which breaks further to SU_3c×U_1em. We use the coset space Sp₄/(SU₂×U₁)×Z₂. The model gives similar predictions for sin²θ_w and proton decay as the minimal SU₅ GUT. Natural choices of parameters suggest that the Higgs masses are as predicted by the Coleman-Weinberg radiative mechanism.