Gauged N = 4 supergravities in five dimensions and their magnetovac backgrounds

Gauged N = 4 supergravity theories with Yang-Mills symmetry SU(2) × U(1) are constructed in five dimensions. As in four dimensions, the presence of a nonsimple gauge group leads to the existence of three distinct theories, depending (in five dimensions) on the values of the SU(2) and U(1) coupling constants. Two of the theories are distinguished by the relative sign of the coupling constants; one of these has a vacuum state exhibiting the full N = 4 anti-de Sitter supersymmetry SU(2,2|2), while the other has a scalar potential with no critical points. The third theory, in which the SU(2) coupling constant is taken to be zero, has vanishing scalar potential. This leads to vacua with spontaneously broken supersymmetry and zero cosmological constant, admitting compactification to four dimensions. All three theories possess “magnetovac” ground states with residual supersymmetry and hence presumably stable. Several of these may be interpreted as four-dimensional cosmological models.     

Parity violation in atoms within left-right symmetric gauge models

Predictions for parity violation in atoms within left-right symmetric theories based on the gauge groups SU(2)_L × SU(2)_R × U(1) and SU(2)_L × SU(2)_L × SU(2)_R × U(1)_L × U(1)_R are presented.     

Electromagnetic properties and decays of Dirac and Majorana neutrinos in a general class of gauge theories

We discuss the electromagnetic properties and decays of Dirac and Majorana neutrinos in a general class of gauge theories. Specific results for the standard SU(2)_L × U(1) and a (not necessarily left-right symmetric) SU(2)_L × SU(2)_R × U(1) theory are analyzed.     

Gauge hierarchy in the presence of discrete symmetry

We discuss the gauge hierarchy problem in theories that posses an additional discrete symmetry. As examples, we consider two models based on the gauge groups U(1)_L×U(1)_Rand SU(2)_L×SU(2)_R×U(1), with parity transformation as the discrete symmetry. By employing a minimal choice of Higgs multiplets there is no freedom, in the semi-classical approximation, to arrange for an arbitrary hierarchy. Either one has a left-right symmetric phase (no hierarchy) or a totally asymmetric phase (infinite hierarchy). It is shown that radiative corrections, à la Coleman-Weinberg, do not smooth out the transition region separating the two phases. A finite gauge hierarchy is not realized.     

Search for a realistic Kaluza-Klein theory

An attempt is made to construct a realistic model of particle physics based on eleven-dimensional supergravity with seven dimensions compactified. It is possible to obtain an SU(3) × SU(2) × U(1) gauge group, but the proper fermion quantum numbers are difficult to achieve.     

Compactification of ten-dimensional superstring theories over Ricci-flat coset spaces

In this paper the compactification of ten-dimensional superstring theories over homogeneous coset spaces S/R is analyzed. We construct explicitly the Ricci-flattening spin connection with torsion for the non-symmetric spaces G₂/SU(3), SU(3)/U(1) × U(1) and Sp(4)/SU(2) × U(1). These spaces provide a solution to the classical field equations with vanishing energy-momentum tensor and therefore one might expect that the conformal invariance of the string theory is preserved. We discuss the two-dimensional non-linear σ-model with Wess-Zumino term corresponding to the homogeneous spaces S/R. In addition, we investigate the constraints for the compactification coming from the requirement of unbroken supersymmetry and anomaly cancellation and give explicit examples of consistent compactification with S and R being embedded into the ten-dimensional gauge group E₈.     

On the structure of the low energy superpotential in superstring theory

We show that after the gauge symmetry breaking of the E₆ grand unified group to the H=SU(3)^c×SU(2)_L×U(1)_Y× U(1)_E subgroup by the Hosotany mechanism a number of additional Yukawa terms not present in a decomposition of 27×27×27 may appear in the low energy superpotential. Some of these terms cause a rapid proton decay.     

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.     

Monopole charges in unified gauge theories

Monopole charges, being global quantities, depend on the gauge group of a theory, which in turn is determined by the representations of all its fields. For example, chromodynamics in its present form when combined with electrodynamics has as its gauge group not SU(3) × U(1) but a “smaller” group U(3). The specification of monopole charges for a theory can thus be quite intricate. We report here the result of an investigation in several current gauge theories. Of particular interest is the possible existence in some theories of monopoles carrying multiplicative charges. As a by-product, we clarify some earlier assertions in the literature which seem to us incorrect.     

On the sign of the n-p mass difference in gauge models

We examine the sign of the n-p mass difference in some gauge models based on the SU(2) × U(1) × U(1) or SU(2)_L × SU(2)_R × U(1) group, and show that a few specific elements of the neutral-vector-meson mass matrix can determine the sign of Δm|_n?p. We also present an SU(2) × U(1) × U(1) model which can give the correct Δm|_n?p.     

Computation of the action for on-shell improved lattice gauge theories at weak coupling

The coefficient in Symanzik's improved lattice action for (pure) SU(2) and SU(3) gauge theories are determined to one-loop order by requiring the absence of leading scaling violations in a set of on-shell quantities, which arise in a world where two dimensions are compactified in a twisted manner.     

Unification of effective field theories

We consider the renormalization of the coupling constants in theories with extended gauge hierarchies. An effective field theory approach is used to include an interesting class of higher-order effects in the renormalization group formulas. We calculate these corrections for all possible breakdowns of O(10) to SU(3)×SU(2)×U(1).     

Progress in lattice gauge theory

Two topics of lattice gauge theory are reviewed. They include string tension and β-function calculations by strong coupling Hamiltonian methods for SU(3) gauge fields in 3 + 1 dimensions, and a 1/N-expansion for discrete gauge and spin systems in all dimensions. The SU(3) calculations give solid evidence for the coexistence of quark confinement and asymptotic freedom in the renormalized continuum limit of the lattice theory. The crossover between weak and strong coupling behavior in the theory is seen to be a weak coupling but non-perturbative effect. Quantitative relationships between perturbative and non-perturbative renormalization schemes are obtained for the O(N) nonlinear sigma models in 1 + 1 dimensions as well as the range theory in 3 + 1 dimensions. Analysis of the strong coupling expansion of the β-function for gauge fields suggests that it has cuts in the complex 1/g²-plane. A toy model of such a cut structure which naturally explains the abruptness of the theory's crossover from weak to strong coupling is presented. The relation of these cuts to other approaches to gauge field dynamics is discussed briefly.The dynamics underlying first order phase transitions in a wide class of lattice gauge theories is exposed by considering a class of models-P(N) gauge theories - which are soluble in the N → ∞ limit and have non-trivial phase diagrams. The first order character of the phase transitions in Potts spin systems for N #62; 4 in 1 + 1 dimensions is explained in simple terms which generalizes to P(N) gauge systems in higher dimensions. The phase diagram of Ising lattice gauge theory coupled to matter fields is obtained in a $\text{1}\text{N}$ expansion. A one-plaquette model (1 time-0 space dimensions) with a first-order phase transitions in the N → ∞ limit is discussed.     

Supersymmetric family unification

The superheavy symmetry breaking of the gauge group in supersymmetrized unified theories is studied. The requirement that supersymmetry be unbroken strongly constraints the possible gauge group breaking, and we systematize such constraints group theoretically.In model building, one issue is whether to permit an adjoint matter superfield with concomitant color exotic fermions. A second issue is that of naturalness which is complicated by the well-known supersymmetry non-renormalization theorems.Both with and without an adjoint matter superfield, the most promising group appears to be SU(9) where three families can be naturally accommodated, at least for low-energy gauge group SU(3)×SU(20×U(1). With an extra U(1) factor, as advocated by Fayet, the non-renormalization theorem must be exploited.     

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.     

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)′.     

Parity violations in hydrogen and the fundamental structure of the weak current

Experiments in progress with hydrogen and deuterium may in practice determine the fundamental parameters and constituents of the weak interaction within the framework of unified gauge theories. In particular, for SU (2) × U (1) theories, from the results of these experiments one can infer the masses of the charged and neutral weak vector bosons (and thus sin²θ_W), and the isospin classification of the right-handed portions of the electron and the u- and d-quarks. Non-singlet assignments for e_R, u_R and d_R would imply the existence of additional leptons and/or quarks. Hydrogen/deuterium data also may be used to discriminate between SU (2) × U (1) models and various models based on larger gauge groups.     

Comments on the derivation of the mixing angles

It is pointed out that Fritzsch's derivation of the mixing angles for a six-quark theory based on a SU(2)_L × SU(2)_R × U(1) model is in error. The correct formula for the mixing angles differs significantly from Fritzsch's results.     

The phase structure of SU(2) × U(1)Y lattice gauge theory

Using analytic and Monte Carlo techniques, we determine the phase structure and nature of spontaneous symmetry breaking of the SU(2) × U(1)_Y electroweak gauge theory with fixed-length Higgs fields on a lattice. We find that it has two completely separated phases: (a) a disordered, symmetric phase and (b) a phase in which SU(2) × U(1)_Y is spontaneously broken to U(1)_em, which is realized in its deconfined Coulomb phase with massless photons. Exact analytic results and approximate series expansions are given for various special cases of the theory.     

Orbifold compactifications with three families of Su(3) ×Su(2) ×U(1)n

We construct several N = 1 supersymmetric three-generation models with SU(3)×SU(2)×U(1)ⁿ gauge symmetry, obtained from orbifold compactification of the heterotic string in the presence of constant gauge-background fields. This Wilson-line mechanism also allows us to eliminate extra colour triplets which could mediate fast proton decay.