The structure of weak interactions for composite quarks and leptons

We consider a model of quarks and leptons as quasi-Goldstone fermions which is based on an underlying supersymmetric SU(2)_HC × SU(2)′_HC preon theory. The spontaneous breakdown of a global U(6) × U(6)′ × U(1) symmetry to U(4) × U(4)′ × SU(2)_diag creates both quarks and leptons and at the same time allows for the possibility of having either residual or fundamental weak interactions. Effective lagrangians in the confining phase of the theory are compared to those emerging from a complementary picture and the problems connected with the nature of the weak interactions are discussed in this context also.     

Supersymmetric preon models with gauged colour-flavour symmetry

We have conducted a search for globally supersymmetric preon models with gauged colour-flavour symmetries. Theories with both two- and three-preon composites, and colour-flavour groups from E₆ down to the standard model, are examined under the following conditions: asymptotically-free metacolour, anomaly-free gauged symmetries, and Pauli principle obeyed. It is found that there are no models with three or more supersymmetric families. If supersymmetry is broken, one model with four families emerges. The purely fermionic preon theories can also be considered as the light sector of a chiral supersymmetric theory, with supersymmetry breaking at the preon level.     

Quasi nambu-goldstone fermions

We explore in detail the hypothesis that quarks and leptons are the approximately massless quasi Goldstone fermions of a supersymmetric preon theory. In particular, we discuss the possible patterns of states emerging from the spontaneous breakdown of global symmetries in supersymmetric theories and construct the low-energy effective lagrangians describing the interaction of these states. In contrast to what happens in the Goldstone sector, the interactions of the quasi Goldstone fermions contain arbitrary parameters which directly reflect the preon dynamics. Various models are explored, including both models in which the weak interactions are residual and models where these interactions are fundamental. A variety of issues are addressed, from the universality and approximate SU(2)_L nature of the weak interactions, for the former class of models, to the generation of states beyond the quarks and leptons and the nature of the dynamical breaking of SU(2)_L×U(1), for the latter class of models. Open questions and speculations connected with the origin of families and the nature of fermion mass generation, including supersymmetry breaking, are also discussed.     

Symmetry breaking in a supersymmetric model of strong and electroweak interactions

We describe a supersymmetric model of strong and electroweak interactions based on the gauge groupSU(3)×SU(2)×U(1)×?(1). We concentrate on the pattern of the spontaneous symmetry breaking by the tree level scalar potential. It is possible to break the?(1) factor at superlarge energies relative to the simultaneous breaking scale ofSU(2)×U(1) and supersymmetry. The model has?(1) anomalies. Attempts to make an anomaly-free model based on the groupE ₆ are described. We also comment on possible modifications of the?(1) anomaly problem due to gravitational effects.     

On goldstone fields in supersymmetric theories

Some aspects concerning the spontaneous breakdown of global internal symmetries in N = 1 supersymmetric theories are discussed. They can be relevant in the context of supersymmetric preon models. We emphasize the connection of Goldstone dynamics to the linear model. Several statements about the number of Goldstone fields are made. The structure of non-linear lagrangians is discussed. In addition, we consider questions concerning complementarity.     

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.     

Unification of families based on a coset space E7/SU(5) × SU(3) × U(1)

We show that the usual three families of quarks and leptons are identifiable with quasi Nambu-Goldstone fermions in a supersymmetric non-linear realization of E₇ corresponding to the Kähler manifold E₇/SU(5) × SU(3) × U(1). So the triplication of families suggests the underlying preon theory realizing the global E₇ linearly. Possible connections with N = 8 supergravity are also discussed.     

XIV. Topology and higher symmetries of the two-dimensional non-linear σ-model

We formulate the O(3) non-linear σ-model and its supersymmetric extension as Abelian gauge theories. As in the Higgs model the instanton number is related to winding properties of the gauge field at infinity. In the new language, a higher symmetry becomes obvious and Pohlmeyer's conserved currents can be derived easily.     

Consequences of the non-abelian anomaly in supersymmetric theories

In supersymmetric theories, the anomalous interactions involving the Goldstone supermultiplets are found not to be determined from symmetry considerations alone: they depend also on the dynamical details of the model. The origin of the unexpected results lies in the presence of the massless fermionic superpartners of the Goldstone bosons. For example, the decay π⁰ → γγ is found to be suppressed in supersymmetric QCD (SQCD). Low-energy effective actions with the correct symmetry properties are constructed, taking SQCD as an illustrative example. The axion decay a → γγ in a supersymmetric composite model might be suppressed with the same mechanism that works for π⁰ → γγ in SQCD.     

Supersymmetric model with an extra U(1) gauge symmetry forbidding proton decay

In the standard model the proton is protected from decay naturally by gauge symmetries, whereas in the ordinary minimal supersymmetric standard model an ad hoc discrete symmetry is imposed for the proton stability. We present a new supersymmetric model in which the proton decay is forbidden by an extra U(1) gauge symmetry. Particle contents are necessarily increased to be free from anomalies, incorporating right-handed neutrinos. Both Dirac and Majorana masses are generated for neutrinos, yielding nonvanishing but small masses. The superpotential consists only of trilinear couplings and the mass parameter &mgr; of the minimal model is induced by spontaneous breaking of the U(1) symmetry.     

Instantons,fermion mass generation and supercomplementarity

We consider the possibility that hypercolor instantons can provide fermion masses in preon models of quark and leptons. After discussing the basic ideas of this mechanism in a non-supersymmetric preon model we consider a supersymmetric, QCD-like preon model. We work within the so-called complementarity picture and show the equivalence between the mass term of the elementary fermions, generated by a vacuum expectation value of a elementary scalar, and the mass term of the composite fermions, generated by the hypercolor instantons.     

On the excited quarks and leptons

Using a duality-like finite energy sum rule, we discuss the assumption of having excited fermions at the W scale in a supersymmetric(SUSY) and non-supersymmetric hypercolour theory where quarks and leptons are bound states of fermion and scalar preon constituents. We conclude that a SUSY-like composite model cannot have excited fermions having a mass smaller than 0.5 TeV. A non-SUSY composite model having composite fermions but elementary W bosons can produce an excited fermion mass of the order of M_W provided that the scalar vacuum condensate is of the order of the (TeV)² scale of compositeness.     

Supercosmology revitalized

Strong coupling effects can avert excess entropy production in supersymmetric models with a large intermediate scale due to symmetry breaking along a flat direction in the effective potential. This is because strong-coupling effects may break supersymmetry giving a large vacuum energy which destabilizes the symmetric field configuration. Alternatively, the reduced number of degrees of freedom in the confined phase destabilized the symmetric field configuration at a high temperature T⪢m_w. This principle is exhibited in a simple supersymmetric flipped SU(5)×U(1) GUT model inspired by the superstring. Compatible scenarios for baryosynthesis are briefly discussed.     

Complete double-projection of light fermion masses in supersymmetric composite models

We present some general classes of supersymmetric models in which the 't Hooft anomaly-matching conditions are precisely satisfied by quasi-Goldstone fermions (QGFs) and hence mass of all the light composite fermions is double-protected by supersymmetry and chiral symmetry. To find this kind of models in an economic way we show that the low-energy spectrum consistent with chiral symmetry is exhausted by QGFs whenever there exists a complementary Higgs picture of the QGF model.     

A supersymmetric extension of the Weinberg-Salam model

By use of Slavnov's procedure, a supersymmetric extension of the Weinberg-Salam model of lepton interactions is obtained. At low energies (E ? m_W), that model is approached very closely. In addition, we get four heavy leptons (m?m_W) and a number of heavy scalars, plus a normally unobservable new neutrino.     

Towards a finite N = 2 susy GUT

We consider finite, N = 2 supersymmetric GUTs based on gauge groups SU(n) and SO(n). As an example, we discuss a semirealistic model based on SO(12). We argue that in finite, N = 2 supersymmetric GUTs, gauge symmetry breaking should occur dynamically. We present a heuristic picture in which this is induced by soft, finiteness preserving SUSY breaking terms. The bound states formed cause a very rapid evolution of the SO(12) coupling constant and break SO(12) into SU(4)×SU(3)_C×U(1).     

Explicit operator solution to thirring model with U(n) symmetry

Two explicit solutions to the Thirring model with U(n) symmetry are constructed following Klaiber's approach. Products of fields are obtained in terms of those for the free case and scale dimensions of composite operators are computed.     

Spontaneous symmetry breaking and Higgs' mechanism in the nonsymmetric Kaluza-Klein theory

The nonsymmetric Kaluza-Klein theory unifying Moffat's theory of gravitation, the Yang-Mills' field and the Higgs' fields are constructed in a geometric manner. Spontaneous symmetry breaking, the Higgs' mechanism and mass generation in the theory are discussed. The connection between R₊ invariance (dilatation on the space-time) from Moffat's theory of gravitation and U(1)_F from GUTs, is proposed within the framework of fermion number conservation.     

Supersymmetric nonlinear sigma models constrained on non-compact manifold

A detailed analysis by 1/n expansion is presented of supersymmetric nonlinear sigma models in two dimensions withU(n) symmetry in which the scalar fields are constrained on a non-compact manifold. The theories are ultraviolet finite. In the massless version of the models no mass scale is generated and gauge bosons fail to get dynamics while this is possible provided the theory contains a mass scale. The effects of introduction of the “Ø-term” into supersymmetric theories are also discussed. In particular, it is argued that supersymmetry is broken by the Ø-term only in finite supersymmetric theories. Finally, a singular behavior in the massless limit in these models is pointed out.     

ChiralSU(7)⊗SU(7) preon model as a hierarchical unification theory

A chiralSU(7) ?SU(7) gauge model is selected out of a wide class of preon models. It contains a pair of chiral preons as well as vectorial ones. Mass splittings of the latter cause rank-retaining breakings of the hyperflavor gauge symmetry in the preonic phase. Hypercolor confinement of preons and the feature of chiral ones among resulting postons (or hyperhadrons) are studied. Rank-decreasing breakings of the hyperflavor symmetry occur successively in the postonic phase as chiral postons acquire dynamical masses. Our coupled equations for quark masses are based on the assumption that electroweak symmetry breaking is due to the cooperation of short-range postonic forces with the infinite-range gluonic one. Updown asymmetry of quark masses are discussed in terms of the equations.