A dynamical theory for the rishon model

We propose a composite model for quarks and leptons based on an exact SU(3)_C × SU(3)_H gauge theory and two fundamental $\text{J=}\text{1}\text{2}$ fermions: a charged T-rishon and a neutral V-rishon. Quarks, leptons and W-bosons are SU(3)_H-singlet composites of rishons. A dynamically broken effective SU(3)_C × SU(2)_L × SU(2)_R × U(1)_B?L gauge theory emerges at the composite level. The theory is “natural”, anomaly free, has no fundamental scalar particles, and describes at least three generations of quarks and leptons.     

Bosonic construction of the Lie algebras of some non-compact groups appearing in supergravity theories and their oscillator-like unitary representations

We give a construction of the Lie algebras of the non-compact groups appearing in four dimensional supergravity theories in terms of boson operators. Our construction parallels very closely their emergence in supergravity and is an extension of the well-known construction of the Lie algebras of the non-compact groups $\text{SP}\text{(2n,}\text{R}$ and $\text{SO}\text{(2n)}{}^1$ from boson operators transforming like a fundamental representation of their maximal compact subgroup U(n). However this extension is non-trivial only for n?4 and stops at n = 8 leading to the Lei algebras of SU(4) × SU(1, 1), SU(1, 1), SU(5, 1), SO(12)¹ and E₇(7). We then give a general construction of an infinite class of unitary irreducible representations of the respective non-compact groups (except for E₇₍₇₎ and SO(12)¹ obtained from the extended construction). We illustrate our construction with the examples of SU(5, 1) and SO(12)¹.     

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 bosons and matter-antimatter oscillations in GUTS

The presence of Higgs bosons of diquark and dilepton types at intermediate mass scales in GUTs is analysed in connection with the possible generation of neutron-antineutron and hydrogen-antihydrogen oscillations. Their renormalization effects on the calculation of the parameters sin²θ_w and m_b/m_τ are investigated in SU(5) and in an SO(10) version with a left-right symmetric breaking chain. In correspondence with suitable combination of higgses, we find solutions in SU(5) for n_G=3 and reasonable values of sin²θ_w, m_b/m_τ and proton lifetime τ_p, which allow detectable $\text{n}\text{-}\text{n}$, but undetectable $\text{H}\text{-}\text{H}$ transitions. Solutions of this type, but with higher τ_p, are also found in a particular scheme of SO(10), where the intermediate mass is at the scale M_R at which the left-right symmetry is broken and is of order 10²×m_w. This modifies then conclusions of analyses of SO(10) models, where either no diquarks and dileptons or only a specific set of them are taken into account.An extension of our analysis to supersymmetric versions of SU(5) and SO(10) does not produce acceptable solutions.     

Composite model of quarks and leptons related to composite structures of SO(10)

It is demonstrated that the composite structure of quarks and leptons can be embedded in the SO(10) model of the strong and electroweak interactions. There appear two entities: two bosonic spinors ξ and ξ′ of SO(4) and a fermionic spinor B of SO(6). All the $\text{16's}$ of fermions can be expressed as (ξjB_α) and $\text{(ξ′j}\text{B}{}^1{}_{\mathrm{\alpha }}\text{)}$, where j=1 or 2 and α=0, 1, 2, 3 indicating the color SU(4) indices. Further consideration leads us to find a basic entity, ζ transforming as 5 under SU(5), of which the charge is $\text{(+}\text{1}\text{2}\text{, 0, ?}\text{1}\text{6}\text{, ?}\text{1}\text{6}\text{) ?}\text{1}\text{6}\text{)}$ and ξ,ξ′ and B can be constructed from ζ and $\text{ζ}$. Although ξ,ξ′ and B obey the SO(10) gauge group, ζ cannot be controlled by SO(10). Some unknown interactions may govern the behavior of ζ at very high energies, where the unification based on SO(10) with ξ,ξ′ and B is destroyed.     

The price of natural flavour conservation in neutral weak interactions

The natural conservation of flavours to O(G_F²) in neutral weak interactions severely constrains choices of gauge groups as well as their fermion representations. In the absence of exactly conserved quantum numbers other than charge, and of |ΔQ| ? 2 charged currents, essentially the only weak and electromagnetic gauge groups whose neutral interactions naturally conserve all flavours are SU(2)_L ? U(1) and SU(2)_L ? [U(1)]². The plausible extensions of these gauge groups to grand unified models including the strong interactions are based on SU(5) and SO(10) respectively. Making the SU(5) model completely natural, including in the Higgs sector, gives the prediction $\text{m}{}_{\mathrm{<mtext>d</mtext>}}\text{/m}{}_{\mathrm{<mtext>e</mtext>}}\text{? m}{}_{\mathrm{<mtext>s</mtext>}}\text{/m}{}_{\mathrm{\mu }}\text{? m}{}_{\mathrm{<mtext>b</mtext>}}\text{/m}{}_{\mathrm{\tau }}\text{? 2605}$ where τ is the probable new heavy lepton and b is the conjectured third flavour of charge $\text{?1}\text{3}\text{quark}$. The SO(10) model contains a potential SU(2)_L ? SU(2)_R ? U(1) weak and electromagnetic gauge group, and has a complicated Higgs structure which does not naturally conserve quark flavours.     

Spontaneous symmetry breaking and fermion chirality in higher-dimensional gauge theory

The number of chiral fermions may change in the course of spontaneous symmetry breaking. We discuss solutions of a six-dimensional Einstein-Yang-Mills theory based on SO(12). In the resulting effective four-dimensional theory they can be interpreted as spontaneous breaking of a gauge group SO(10) to $\text{H}\text{=}\text{SU}\text{(3)}{}_{\mathrm{<mtext>C</mtext>}}\text{×}\text{SU}\text{(2)}{}_{\mathrm{<mtext>L</mtext>}}\text{×}\text{U}\text{(1)}{}_{\mathrm{<mtext>R</mtext>}}\text{×}\text{U}\text{(10)}{}_{\mathrm{B?L}}$. For all solutions, the fermions which are chiral with respect to $\text{H}$ form standard generations. However, the number of generations for the solutions with broken SO(10) may be different compared to the symmetric solutions. All solutions considered here exhibit a local generation group SU(2)_G × U(1)_G. For the solutions with broken SO(10) symmetry, the leptons and quarks within one generation transform differently with respect to SU(2)_G × U(1)_G. Spontaneous symmetry breaking also modifies the SO(10) relations among Yukawa couplings. All this has important consequences for possible fermion mass relations obtained from higher-dimensional theories.     

Flavour and superunification

We consider the possibility of a non-trivial embedding of $\text{(}\text{10}\text{+}\text{5}\text{)}\text{SU}\text{(5)}$ families of spin if$\text{1}\text{2}$ left-handed fermions in a combination of irreducible massless supermultiplets of N extended supersymmetry. We demand the whole spectrum of spin $\text{1}\text{2}$ states to be anomaly free with respect to SU(N). This turns out to be a necessary condition for the absence of anomalies at the SU(5) level. We find two classes of models, with spin $\text{1}\text{2}$ fermions in SU(N) representations associated to one- and two-column Young tableaux, respectively, in which each irreducible massless multiplet occurs at most once. These two classes of models lead to a nontrivial family generation due to supersymmetry. For N = 8 extended supersymmetry, they give at most three and five families, respectively. The first class of models is more natural in the way it excludes SU(5) exotics. The same analysis is extended to the massless multiplets that can be obtained from bilinear composite fields of the (preonic) elementary fields of N extended supergravity. We prove that the generation of families requires the repetition of massless multiplets and that ($\text{10 +}\text{5}$) SU(5) families can only be generated in pairs. General properties of multilinear composite operators of the preonic fields are given and the rôle of massive representations to classify towers of operators with definite spin is pointed out.     

Chiral fermion generations from higher-dimensional gravity

We discuss a six-dimensional SO(12) gauge theory which can be obtained from pure gravity in 18 dimensions coupled to a Majorana-Weyl spinor, if the ground state is characterized by a noncompact internal space without boundary with small finite volume. The six-dimensional SO(12) theory spontaneously compactifies to a four-dimensional SO(10) theory with local generation group SU(2)_G × U(1)_G. We obtain an even number of chiral fermion generations transforming as ($\text{16, k, ±}\text{1}\text{2}$) under SO(10) × SU(2)_G × U(1)_G. Adding a scalar field to the six-dimensional theory provides us with fields carrying all the quantum numbers needed for a realistic spontaneous symmetry breakdown to SU(3)_c × U(1)_e.m.     

SU(3) ⊗ SU(2) ⊗ U(1) from D = 11 supergravity

In this paper we show that D = 11 supergravity admits an infinite discrete class of solutions having the phenomenological group SU(3) ? SU(2) ? U(1) as a symmetry of the internal space M₇. These solutions lead, in dimensional reduction, to SU(3) ? SU(2) ? U(1) gauge fields.In general all these spaces produce a complete breaking of supersymmetry except in one case where N = 2 supersymmetry survives. The parameter which classifies the solutions is a rational number q/p which describes the embedding of the stability subgroup SU(2) ? U(1) ? U(1) of M₇ in SU(3) ? SU(2) ? U(1). For all q/p ≠ 1 the holonomy group is SO(7) and all supersymmetries are broken. For q/p = 1 the holonomy group is SU(3) and two supersymmetries survive. In this last case we can also find a solution with internal photon curl $\text{F}{}_{\mathrm{\alpha \beta \gamma \delta }}\text{≠ 0}$. It breaks all sypersymmetries.     

SU (4) × SU (4) symmetry breaking and its implications for SU (3) × SU (3) breaking

We investigate models where the SU (4) × SU (4) symmetry breaking Hamiltonian, $\text{H}$_SB, belongs to the (15, 15) and $\text{(10,}\text{10}\text{) + (}\text{10}\text{, 10)}$ representations, and show how they are equivalent to models of SU (3) × SU (3) breaking where $\text{H}$_SB belongs to a mixture of different representations. The results for the ππ scattering lengths in the (15, 15) model are outside the experimental limits, but the $\text{(10,}\text{10}\text{) + (}\text{10}\text{, 10)}$ model yields solutions with a wide range of values for the scattering lengths within the experimental bounds.     

Stability of higher-dimensional Einstein-Yang-Mills theories on symmetric spaces

We study (4 + d)-dimensional Einstein-Yang-Mills theories with arbitrary gauge groups, G_YM. The theory is compactified on a d-dimensional symmetric coset space $\text{G}\text{H}$ with a symmetric, topologically non-trivial classical gauge field, embedded in an H-subgroup of the Yang-Mills group. These theories are known to be classically stabilized by gravity if G_YM = H, $\text{G}\text{H}$ is a sphere and d ≠ 3. We study classical instabilities caused by embedding H in a larger gauge group. The small fluctuation spectrum is completely calculable, and leads to a stability condition. For two-dimensional spheres this condition is precisely the Brandt-Neri stability condition for non-abelian monopole fields. For four-spheres we find stability for SU(2) instantons embedded in arbitrary gauge groups and we reproduce the fluctuation spectrum around instantons. For higher-dimensional spheres the stable solutions of this type are completely classified, and occur only for d = 5, 6, 8, 9, 10, 12 and 16. The results show a remarkable agreement with expected topological stability. We also give a few examples with other symmetric spaces, such as CP_n, where the stability criterion appears less restrictive.     

Unified theory of weak and electromagnetic interactions with ΔI = 12 rule

An SU(2) ? U (1) gauge theory of weak and electromagnetic interactions satisfying the $\text{ΔI =}\text{1}\text{2}$ rule is proposed, which has the following characteristic: (i) A neutral boson Z, coupling to the neutral strangeness-changing current is used in addition to the usual charged ones, to give the $\text{ΔI =}\text{1}\text{2}$ rule in the standard fashion. Couplings are chosen such that the Z decouples from the observed leptons, in order to agree with experiment. (ii) It is assumed that the |ΔY| = 2 transitions due to neutral vector-boson exchange cancel the |ΔY| = 2 contributions due to charged vector-boson exchange. This constraints the Cabibbo angle in a manner consistent with experiment.     

A new representation for the density matrix: (II). Equations of motion

The equations of motion for the new SU(n) parameters representing the density matrix for arbitrary spin are derived. It is shown that for a class of hamiltonians which are diagonal, the equations are exactly solvable by using the device of combining the SU(n) parameters in pairs using the Pauli spin matrix σ_y. It is also shown that using the correspondence relations between the SU(n) parameters and the spherical tensor moments, it is possible to picture the time evolution of the tensor parameters using the explicit solutions for the SU(n) parameters. This procedure has been illustrated by discussing in detail the problem of spin-1 and $\text{spin}\text{-}\text{3}\text{2}$ systems interacting with an external magnetic field and subjected to quadrupole interactions.     

Exact SU(n) instantons with cylindrical symmetry

We construct SO(3) symmetric, irreducible instantons in an SU(n) gauge theory. The solutions are symmetric with respect to J = ?ir × ? + T, where T spans the maximal SO(3) subalgebra of SU(n). Our ansatz as well as the resulting self dual equations are closely related to those for monopoles.     

Surface representations of Wilson loop expectations in lattice gauge theory

Expectations of Wilson loops in lattice gauge theory with gauge group $\text{G}\text{=}\text{Z}{}_2$, U(1) or SU(2) are expressed as weighted sums over surfaces with boundary equal to the loops labelling the observables. For $\text{G}\text{=}\text{Z}{}_2$ and U(1), the weighted are all positive. For G = SU(2), the weights can have either sign depending on the Euler characteristic of the surface. Our surface (or flux sheet-) representations are partial resummations of the strong coupling expansion and provide some qualitative understanding of confinement. The significance of flux sheets with nontrivial topology for permanent confinement in the SU(2)-theory is elucidated.     

SU(2)×U(1) effects in e+e− annihilation: Generalized charge asymmetry

The observability of the SU(2)×U(1) electroweak charge asymmetry effects in e⁺e^? annihilation at $\text{s}\text{=29}\text{GeV}$ is addressed in the context of a Feynman-Field type fragmentation model. We assume three colors of five flavored quarks and one heavy lepton τ. We neglect, at this time, the hard gluon bremsstrahlung events. We take b→c+X as the b-decay mode and we assume all τ's and heavy hadrons decay within the resolution of the detector so thatonly light hadrons and leptons are detected. Allowing all these decays to occur, we then compute the expected front-back asymmetry of negatively charged particles weighted with zⁿ for z?0.0175, where n = 0.5, 1…, 7, 10, and z is the light-cone momentum fraction. We find, for example, that such an asymmetry is ≈5% for n=2for sin²θ_w=0.236 and Λ_{QCD=0.34 GeV}. In other words, due to the large number of charge particles produced per event, this SU(2)×U(1) charge asymmetry may be accessible experimentally in e⁺e^? → X already at PEP and PETRA energies.     

Complex Cabibbo angle and CP violation in a class of gauge theories

A class of gauge theories which incorporate CP violation is discussed. The CP violating effects arise as a consequence of performing a different rotation in the SU(3) space for the left- and right-handed strangeness conserving charged currents. It is suggested that it is possible to understand the smallness of these effects in the $\text{K}{}_0\text{?}\text{K}{}_0$ system even in the presence of a large relative phase between the left- and right-handed weak currents. The electric dipole moments of hadrons are of fifth order in the semi-weak coupling constant whereas for leptons they are of seventh order. These electric dipole moments are considerably smaller than the experimental upper limits.     

Towards a canonical fermi mass matrix for a pure generation structure

Vertical constraints on the horizontal generation structure are discussed. The minimal electro/nuclear scheme for which the generation structure must be pure is identified to be the partially unified Pati-Salam SU(4)_C×SU(2)_L×SU(2)_R. SO(10) type unification furthermore requires the horizontal group factor to be axial. This in turn crucially affects the Yukawa couplings in such a way that a minimal Higgs system with only two conventional scalars is capable of uniquely giving rise to the ‘canonical’ Fritzsch-type mass matrix, for any arbitrary number of fermionic families. The anomaly-free equations then provide the desired one-to-one correspondence between the mass matrices in the two charged quark sectors. The derived horizontal quantum numbers suggest that the maximal horizontal group factor be SU(2), with the generations furnishing two neighbor $\text{j}\text{and}\text{j +}\text{1}\text{2}$ representations. Finally, a careful phase analysis shows that the tree-level soft and superwork CP-violation solely reflects the non-abelian character of the horizontal group, representing an induced internal rotation which is triggered by the phase elimination performed in the vertical sector.     

Supersymmetric flipped SU(5) revitalized

We describe a simple N = 1 supersymmetric GUT based on the group SU(5)×U(1) which has the following virtues: the gauge group is broken down to the SU(3)_C×SU(2)_L×U(1)_Y of the standard model using just 10, $\text{10}$ Higgs representations, and doublet-triplet mass splitting problem is solved naturally by a very simple missing-partner mechanism. The successful supersymmetric GUT prediction for sin²θ_w can be maintained, whilst there are no fermion mass relations. The gauge group and representation structure of the model may be obtainable from the superstring.