Unified Gauge Group Research Articles

Supergravity-induced E8 gauge hierarchies.

We consider the gauge breaking of supergravity-based E/sub 8/ grand unified gauge group to E/sub 6/ in the zeroth order of supergravity at Planck mass scale M and E/sub 6/ to SO(10) at a scale xi, where xiis a small supergravity expansion parameter of the order of 10/sup -4/. Then surprisingly we find that the subsequent breaking of SO(10) to SU(5), SU(5) to G/sub std/(equivalentSU(2)/sub L/ x U(1)/sub Y/ x SU(3)/sub C/), and G/sub std/ to G/sub L//sub E/(equivalentSU(3)/sub C/ x U(1)/sub Q/) occur at scales xi2''M, xi2numberM, and xi2$M, respectively, with local supersymmetry breaking at the weak scale in the visible sector.

A SCALAR-TENSOR THEORY FOR INDUCED GRAVITY

A scalar-tensor theory for induced gravity is presented. Einstein's gravity appears as the low-energy limit of such a theory. It is shown that the spontaneous symmetry breaking can occur at any epoch of the universe and that this mechanism can also be responsible for breaking the unified gauge group SU(5) into SU (3) × SU (2) × U (1). Also, it is shown that, if the spontaneous symmetry breaking is accomplished by means of the Coleman-Weinberg potential minimum, the induced gravitational constant can, with a suitable choice of the coupling function, increase as one dates back.

Fermion masses in E 8 × E′ 8 superstring theories

We consider string theories with gauge group E 8 × E′ 8 compactified on Calabi-Yau manifolds so that the unified gauge group is E 6 × E′ 8. If the fermion content is Ninf · 27 + δ (27 + 27 ), where δ = 1 or 2, and the E 6 is broken by Wilson loops to a gauge group Σ (which contains SU(3) c × SU(2) L × U(1) y ), then Σ is specified almost uniquely if we require that neither the up nor the down quark mass matrices are identically zero at tree level and that the Higgs doublets arise via the incomplete multiplet mechanism. In particular, Σ must be rank 6. However, if we wish for the neutral mass matrix to be acceptable, we must have the electron mass matrix identically zero at tree level. We comment on a way to possibly have small (but non-zero) neutrino masses in superstring models.

Supersymmetric models for quarks and leptons with nonlinearly realized E

We propose three supersymmetric nonlinear sigma models with global symmetry E/sub 8/. The models can accommodate three left-handed families of quarks and leptons without incurring the Adler-Bell-Jackiw anomaly with respect to either the standard SU(3) x SU(2) x U(1) gauge group, or the SU(5), or SO(10) grand unifying gauge group. They also predict unambiguously a right-handed, fourth family of quarks and leptons. In order to explore the structure of the models, we develop a differential-form formulation of the Kahler manifolds, resulting in general expressions for the curvature tensors and other geometrical objects in terms of the structure constants of the algebra, and the squashing parameters. These results, in turn, facilitate a general method for determining the Lagrangian to quartic order, and so the structure of the inherent four-fermion interactions of the models. We observe that the Kahlerian condition d..omega.. = 0 on the fundamental two-form ..omega.. greatly reduces the number of the independent squashing parameters. We also point out two plausible mechanisms for symmetry breaking, involving gravity.

Monopolonium

We examine the general properties of a monopole anti-monopole bound state. Lifetimes grow as the cube of the initial diameter and range, for an SU(5) GUT monopole with mass = 2 × 10 16 GeV, from about 43 days for d = 1 fm, to 10 11 years for d = 0.1 angstrom. We find about 10 7 hadrons are produced by fragmentation of gluons that are radiated by classical Larmor radiation. In the final burst when the extended cores overlap about 25 fundamental degrees of freedom of the full unified gauge group are produced. We find that such objects would have been produced in the early universe at about the time of helium synthesis and their decay products and Larmor radiation may be observable.

Early unification and the Weinberg angle in the SU(4) 4 grand unified model

In the framework of the grand unified gauge group SU(4) 4 we discuss possibilities to reconcile the low unification scale (10 5−10 7 GeV) with the acceptable value of sin 2 θ w. We consider various specific models which differ by the values of the intermediate mass scale, the choice of the fermion multiplets and by the embedding of the electroweak group SU(2) into SU(4) 4. The class of theories with early unification and correct sin 2 θ w is constructed. They all predict new non-sequential fermions which are SU(2) L,R singlets and have unconventional electric charges. Cosmological implications of such theories are discussed and it is argued that new particles may well account for the positive results of searches for fractional charge in terrestrial matter.

Locally Supersymmetric Grand Unification

A locally supersymmetric grand unification program is proposed which couples the $N=1$ supergravity multiplet to an arbitrary grand unified gauge group with any number of left-handed chiral multiplets and a gauge vector multiplet. A specific model is discussed where it is shown that not only do the gravitational interactions eliminate the degeneracy of the vacuum state encountered in global supersymmetry, but simultaneously they can break both supersymmetry and SU(2) \ensuremath{\bigotimes} U(1) down to a residual $\mathrm{SU}{(3)}^{c}\ensuremath{\bigotimes}\mathrm{U}(1)$ symmetry at \ensuremath{\sim}300 GeV.

Baryon asymmetry and the scale of supersymmetry breaking

I discuss the constraints on supersymmetric grand unified theories (SSGUT's) imposed by requiring that such theories be compatible with the presently observed baryon asymmetry of the Universe. I concentrate on those SSGUT's in which the scale of supersymmetry breaking is small compared to the scale at which the baryon asymmetry is generated. If one neglects the supersymmetry breaking, most models of this kind have, at zero temperature, degenerate vacuums which include the gauge-symmetric ground state. In general, it is very hard to obtain a realistic scenario for the phase transitions of these models in the early Universe (i.e., at large temperatures). One of thereasons for this difficulty is due to the following theorem: In SSGUT models with a simple unifying gauge group, one cannot have a situation in which the gauge symmetry decreases as the temperature is raised (in a regime where the coupling constant is small). I argue that if supersymmetry is relevant in grand unified models, it is probably broken at a fairly high scale---above the scale of baryon-number generation.

Effective parameters and the renormalization group in grand unified theories

A straightforward determination of the low-energy effective gauge couplings of the light effective theories which result from the breakdown of a simple unifying gauge group is presented. The procedure utilizes the decoupling equation, which has been proved to all orders in previous papers. The method developed is applied to the minimal SU(5) model to calculate ${{sin}^{2}\ensuremath{\theta}}_{w}$, with two-loop Higgs effects included. The difference between the physical and minimally subtracted $X$-gauge boson mass is also evaluated.

A new criterion for constructing SU( N) grand unified models and residual discrete symmetry

It is pointed out that there exists a residual discrete symmetry when a grand unified gauge group is broken down to G 1=SU(3)×SU(2)×U(1) at a mass scale of the order of 10 15 GeV through a concrete Higgs mechanism. This residual symmetry prevents some fermions from receiving masses of the order of 10 15 GeV, so the gauge group can accommodate more low-mass fermions. We discuss some examples based on the Higgs mechanism with residual symmetry.

On the suppression of monopole production in the very early universe

We investigate the effects of thermal fluctuations near the phase transition corresponding to the breakdown of a grand unified gauge group G to G′ × U(1) in the very early Universe, especially as regards the production of superheavy monopoles. Using SU(5) as a generic example of a grand unified theory, we find that this will be strongly suppressed for a reasonable range of parameters appearing in the Higgs potential. Allowing for a dynamical Higgs mechanism, leading to a considerable ratio of Higgs particle to leptoquark boson masses, the number of produced monopoles will be negligible.

A model for electroweak interactions based on the left-right symmetric gauge group U L(2) ⊗ U R(2)

The left-right symmetric gauge group U L(2) ⊗U R(2) is considered as the unifying electroweak gauge group. It is shown that it has the merit of fixing the mixing parameter sin 2θ W of the standard model at 0.25.

Massless fermion representations in grand unified gauge theories

A classification is given of fermion representations of grand unified gauge groups for which gauge-invariant mass terms are forbidden. An explicit global invariance which requires neutrinos to be massless is found for models based on the grand unified groups SU(5) and E6.

The two neutral currents of the unified gauge group SU(6)

The assignment of ν μ to the 6 representation of SU(6) allows to explain the neutral current deep inelastic data and the absence of parity violation in atoms. The effective neutral currents coupled to the two neutrinos are different.

Gauge-coupling-constant magnitudes in the Pati-Salam model

A doubly tiered hierarchy of symmetry breaking is proposed in which a unified gauge group is broken first to the Pati-Salam group SU(2)/sub L/ x SU(2)/sub R/ x SU(4), subsequently to the SU(2)/sub L/ x U(1) x SU(3)/sub c/ group containing the known elementary-particle interactions. The second level of symmetry breaking corresponds to the differentiation of baryon number from lepton number. Such a hierarchy is consistent with the phenomenology of the Pati-Salam model for integrally charged quarks. The proposed hierarchy allows the weak angle to remain in the range 3/8 < or = sin/sup 2/theta/sub W/ < or = 0.42 as the quark-gluon coupling constant becomes appropriately large. It is suggested that the first level of symmetry breaking corresponds to the separation of gravity from elementary-particle interactions. The hierarchy is also shown to apply for fractionally charged quarks, increasing the quark-gluon coupling constant (..cap alpha../sub s/ approx. = 0.1) while leaving the weak angle sin/sup 2/theta/sub W/ approx. = 3/8.

Neutrino data, exotic quarks and higher groups

It is pointed out that the principle of natural conservation of strangeness and present neutrino data motivate the consideration of models with exotic quarks or the enlargement of the unifying gauge group beyond SU(2) ⊗ U(1).

S U(6) as a Unified Gauge Group

S U(6) as a Unified Gauge Group

SU(6) as a Unifying Gauge Group and CP-violation

SU(6) as a Unifying Gauge Group and CP-violation