Baryon number generation in a flipped SU(5) × U(1) model

We consider the possibilities for generating a baryon asymmetry in the early universe in a flipped SU(5) × U(1) model inspired by the superstring. Depending on the temperature of the radiation background after inflation we can distinguish between two scenarios for baryogenesis: (1) after reheating the original SU(5) × U(1) symmetry is restored, or there was no inflation at all; (2) reheating after inflation is rather weak and SU(5) × U(1) is broken. In either case the asymmetry is generated by the out-of-equilibrium decays of a massive SU(3) × SU(2) × U(1) singlet field φ_m. In the flipped SU(5) × U(1) model, gauge symmetry breaking is triggered by strong coupling phenomena, and is in general accompanied by the production of entropy. We examine constraints on the reheating temperature and the strong coupling scale in each of the scenarios.     

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)′.     

A symmetry reduction scheme of the Dirac algebra without dimensional defects

In relating the Dirac algebra to homogeneous coordinates of a projective geometry, we present a simple geometric scheme which allows to identify various Lie algebras and Lie groups well-known from classical physics as well as from quantum field theory. We introduce a 1 -point-compactification and quaternionic Möbius transformations, and we use SU* (4) and a symmetry reduction scheme without dimensional defects to identify transformations and particle representations thoroughly. As such, two subsequent nonlinear σ models SU*(4)/U Sp(4) and U Sp(4)/SU(2) × U(1) emerge as well as a possible double coset decomposition of SU*(4) with respect to SU(2) × U(1). Whereas the first model leads to equivalence classes of hyperbolic manifolds and naturally introduces coordinates and velocities, the second coset model leads to a Hermitian symmetric (vector) space (Kählerian space) of real dimension 6, i.e., to a 3-dimensional complex space with a global symplectic and a local SU(2) × U(1) symmetry which allows to identify the (local) gauge group of electroweak interactions as well as under certain assumptions it admits compact SU(3) transformations as automorphisms of this 3-dimensional (hyper)complex vector space. In the limit of low energies, this geometric SU*(4) scheme naturally yields the (compact) group SU(4) to describe “chiral symmetry” and conserved isospin of hadrons as well as the low-dimensional hadron representations. Last not least, with respect to some of the SU*(4) generators we find a multiplication table which (up to signs) is identical with the octonions represented in the Fano plane.     

Is U(1)H a good family symmetry?

We analyze U(1)_H as a horizontal symmetry and its possibilities to explain the known elementary-fermion masses. We find that only two candidates, in the context of SU(3)_c ? SU(2)_L ? U(1)_Y ? U(1)_H nonsuper-symmetric, are able to fit the experimental result m_b«m_t. identity, but it is a common prejudice to assume that the appropriate family symmetry may explain this fact as a consequence of (i) and (ii). In what follows we will enlarge the SM gauge group with an extra U(1)_H horizontal local gauge symmetry (the simplest multi-family continuous symmetry we can think of). We then show that the structure SU(3)_c ? SU(2)_L ? U(1)_Y ? U(1)_H by itself is able to explain (ii), and that the simplest supersymmetric (SUSY) extension of this model without a μ-term can not cope with (ii).     

STRING THEORY WITH THREE FAMILIES OF CHIRAL FERMIONS

A heterotic string theory is constructed by compactifying directly from 26 to 4 dimensions via a smooth manifold T²²/G. In the low energy limit, there are three families of chiral fermions with exactly the same quantum numbers as thatin the standard supersymmetric SU(3)×SU(2)×XU(1) model. They couple to supergravity and supergauge fields with the gauge symmetry SU(3)_F×SU(3)_c×SU(3)_L×U(1)_YR×U(1)_I3R.     

Broken colour symmetry and liberated quarks

We present and discuss a quark model of hadrons, in which local SU(3) gauge symmetry is completely broken and yet asymptotic freedom is presented. There is no infrared slavery in this model, and isolated quarks are free to exist. Colour becomes a global symmetry which is only approximate under SU(3) but nearly exact under SU(2) × U(1), as far as the usual hadron spectroscopy is concerned.     

An orbifold compactification with three families from twisted sectors

We obtain a three generational SU(3)_c×SU(3)_w×U(1)⁴×[SO(12)×U(1)²]′ model from an orbifold construction with the requirement that three generations arise from twisted sectors. There exist supersymmetric vacua realizing the standard model. In one example the anomalous U(1) breaks the gauge symmetry down to SU(3)_c×SU(3)_w×U(1)_y×SO(12)′.     

Operator analysis of proton decay in an SU(7) gut

An SU(7) model, with a surviving low-energy SU(4) × SU(3) × U(1) gauge symmetry, may reduce the number of low-energy effective four-fermion baryon number violating interactions from six to two. A simple argument, applicable to general SU(N), shows that the terms allowed by SU(4) × SU(3) × U(1) are the same as those allowed by SU(7).     

Higgs couplings in the integer-charge quark model

Colour SU(3) symmetry is broken spontaneously by the introduction of coloured Higgs scalars in the standard SU(3)×SU(2)×U(1) model, so as to make the quarks integrally charged. The resulting couplings of the Higgs bosons with the gauge bosons are worked out.     

A classification of compactifying solutions for d =11 supergravity

Supergravity in eleven dimensions is known to have classical solutions of the type (anti-de Sitter space-time) × (7-dimensional Einstein space). We give a list of all homogeneous 7-manifolds which admit an Einstein metric. Known solutions are reviewed, with some emphasis on the SU(3) × SU(2) × U(1) compactifications. Their topology is discussed in detail.The list includes three new solutions, with symmetry groups SU(3) × SU(2), SO(5) and SO(5) × U(1). The first solution has no supersymmetry, while the second and third yield respectively N = 1 and N = 2 supersymmetry in four dimensions. The last two solutions may be extended to solutions with nonzero internal photon curl, breaking all supersymmetry.The existence of a spin structure on homogeneous manifolds $\text{G}\text{H}$ is discussed and related to topological properties of $\text{G}\text{H}$. As an illustration, we treat the coset spaces SU(m + 1) × SU(n + 1)/SU(m) × SU(n) × U(1), which include the spaces with SU(3) × SU(2) × U(1) symmetry.     

Higgs fields and the determination of the Weinberg angle

SU(2) × U(1) gauge theories, in which the Higgs fields transform as doublets under SU(2) are interpreted as pure Yang-Mills theories in six dimensions, the components of the gauge potentials in the extra dimensions playing the role of the Higgs' fields. Two consistent theories are discovered: one in which SU(2) × U(1) is embedded in SU(3) and the vector bosons remain massless - and another where SU(2) × U(1) is embedded in the graded Lie algebra SU(2|1), the symmetry is spontaneously broken in a natural fashion and the theory is equivalent to that of Weinberg and Salam, with a specific value 30° for the Weinberg angle and a prediction of the Higgs' mass.     

Spontaneous breaking of chiral symmetry in QCD

The consistency of iso-spin (SU(3)) symmetry of the vacuum with the spontaneous breakdown of chiral symmetry without the appearance of a U(1) Goldstone boson, is investigated.     

The link between the emergence of the GIM mechanism and the nature of the neutral-current parity violation

We show that minimization of the Higgs potential within the unifying symmetry [SU(4)]⁴ together with the requirement that the GIM mechanism should emerge as a consequence of spontaneous breakdown of the symmetry on the flavor side leaves us with onechoice regarding the nature of parity violation: charged current as well as neutral current parity violations must have one and the same origin; if the former is à la SU(2)_L×U(1), so must be the latter. Furthermore, there appear to be only two possible alternative forms for the low-energy electroweak symmetry: (i) the familiar SU(2)_L×U(1), and (ii) and extended symmetry SU(2)_L×U(1)_L×?(1)_R differing from the former only in the parity-conserving neutral current sector.     

The SU(8) GUT for chiral families

We argue that there is a natural inclusion of the standard model with the family-unified chiral local symmetry SU(3)_H in a new SU(8) GUT inspired by Georgi's SU(11) model. The SU(8) symmetry breaking along the chain with the intermediate electro-weak-horizontal unification SU(8)→SU(5)_EWH×SU(3)_c×U(1) is proved d to be the distinguished pattern. The model predicts a long-lived proton (10³³–10³⁵yr) and practically the observed value of the Weinberg angle, in sharp contrast to the ordinary GUTs. The observation of the specific flavour-changing baryon decays (p→π,μ,Ke,…) could unambiguously single out the flavour unified GUTs as well as confirm the existence of the elementary horizontal forces at small distances.     

ELECTRO-WEAK UNIFIED TNEQRY AND RELATED PROBLEMS

The minimum SU(2)×U(1) electro-weak unified theory is described and several related problems including the connection between anomaly free and charge quantization, Kobayashi-Maskawa mixing and CP violation and Higgs sector are dis-cussed. The experimental verification minimum of SU(2)×U(1) model in low energy range is presented briefly. Physical conseguences concerning to free W and Z particles are discussed. The possibilities of the existence or gauge symmetry higher than SU(2)×U(1) for electro-weak interaction and with the minimum SU(2)×U(1) model as the first order of approximation in the low energy range are given. New phenomena involving Z Partice and their implication based on SU(2)×U(1) model are examined.     

A SUPERSYMMETRICAL PREON MODEL WITH SU(2)L × SU(2)R ×U(1)B-L SYMMETRY BROKEN BY COUPLING TO SUPERGRAVITY

A supersymmetrical preon model is proposed. In this model there are Higgs particles which are massless at the scale of confinement of hypercolor due to the supersymmetry and a discrete R symmetry. We show that in this model the low energy gauge symmetry SU(2)_L×SU(2)_R×U(1)_B-L can be broken to U(1)_Q at the scale of supersymmetry breaking by coupling to supergravity.     

Axions from chiral family symmetry

We investigate the possibility that family symmetry, G_F, is spontaneously broken chiral global symmetry. We classify the interesting cases when family symmetry can result in an automatic Peccei-Quinn symmetry U(1)_PQ and thus provide a solution to the strong CP problem. The result disfavors having two or four families. For more than four families, U(1)_PQ is in general automatic. In the case of three families, a unique Higgs sector allows U(1)_PQ in the simplest case of G_F = [SU(3)]³. Cosmological consideration also puts strong constraint on the number of families. For G_F = [SU(N)]³ cosmology singles out the three-family (N = 3) case as a unique solution if there are three light neutrinos. Possible implication of decoupling theorem as applied to family symmetry breaking is also discussed.     

A study of SU(3) × SU(2) × U(1) × U(1) as an intermediate energy subgroup of SO(10)

We analyze several patterns of symmetry breaking of SO(10) where SU(3)_c × SU(2) × U(1) × U(1) is an intermediate energy subgroup. Using constraints from the renormalization group and data from neutral-current experiments we show that if the only Higgs used in the low-energy breaking of the theory are those which can give mass to fermions then the possibility of a low intermediate mass scale is ruled out.     

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.     

Flipped SO(10)

We constract an N = 1 supersymmetric SO(10) GUT broken down to SU(3)_c×SU(2)_L×U(1)_Y with an intermediate flipped SU(5)×U(1)_X gauge symmetry. A solution to the triplet-doublet mass-splitting problem is proposed in terms of a non-minimal missing-partner mechanism.