Grand Unified Gauge Group Research Articles

Classification of three-family grand unification in string theory. II. The SU(5) and SU(6) models

Requiring that supersymmetric SU(5) and SU(6) grand unifications in the heterotic string theory must have 3 chiral families, adjoint (or higher representation) Higgs fields in the grand unifiedgauge group, and a non-abelian hidden sector, we construct such string models within the framework of conformal field theory and asymmetric orbifolds. Within this framework, we construct all such string models via Z_6 asymmetric orbifolds that include a Z_3 outer-automorphism, the latter yielding a level-3 current algebra for the grand unification gauge group SU(5) or SU(6). We then classify all such Z_6 asymmetric orbifolds that result in models with a non-abelian hidden sector. All models classified in this paper have only one adjoint (but no otherhigher representation) Higgs field in the grand unified gauge group. This Higgs field is neutral under all other gauge symmetries. The list of hidden sectors for 3-family SU(6) string models are SU(2), SU(3) and $SU(2) \otimes SU(2)$. In addition to these, 3-family SU(5) string models can also have an SU(4) hidden sector. Some of the models have an anomalous U(1).

Grand unification with three generations in free fermionic string models.

We examine the problem of constructing three generation free fermionic string models with grand unified gauge groups. We attempt the construction of $G\times G$ models, where $G$ is a grand unified group realized at level 1. This structure allows those Higgs representations to appear which are necessary to break the symmetry down to the standard model gauge group. For $G=SO(10)$, we find only models with an even number of generations. However, for $G=SU(5)$ we find a number of 3 generation models.

Higgs and super-Higgs effects with naturally vanishing classical vacuum energy

We construct N = 1 supergravity models where the gauge symmetry and supersymmetry are both spontaneously broken, with naturally vanishing classical vacuum energy and unsuppressed Goldstino components along gauge non-singlet directions. We discuss some physically interesting situations where such a mechanism could play a role, and identify the breaking of a grand-unified gauge group as the most likely possibility. We show that, even when the gravitino mass is much smaller than the scale m x of gauge symmetry breaking, important features can be missed if we first naively integrate out the degrees of freedom of mass O( m x ), in the limit of unbroken supersymmetry, and then describe the super-Higgs effect in the resulting effective theory. We also comment on possible connections with extended supergravities and realistic four-dimensional string constructions.

Planck-scale unification and dynamical symmetry breaking.

We explore the possibility of unification of gauge couplings near the Planck scale in models of extended technicolor. We observe that models of the form $G\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(3)}_{c}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{U}(1)}_{Y}$ cannot be realized, due to the presence of massless neutral Goldstone bosons (axions) and light charged pseudo Goldstone bosons; thus, unification of the known forces near the Planck scale cannot be achieved. The next simplest possibility, $G\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(4)}_{\mathrm{PS}}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{U}(1)}_{{T}_{3R}}$, cannot lead to unification of the Pati-Salam and weak gauge groups near the Planck scale. However, superstring theory provides relations between couplings at the Planck scale without the need for an underlying grand-unified gauge group, which allows unification of the ${\mathrm{SU}(4)}_{\mathrm{PS}}$ and ${\mathrm{SU}(2)}_{L}$ couplings.

Probing the symmetry-breaking pattern using sfermion masses

We study the mass spectrum of superparticles within supersymmetric grand unified models. For gaugino masses, it is pointed out that the GUT relation in the SU(5) model is applicable to a more general case where a grand-unified gauge group breaks dowm to the standard model gauge group by several steps. We also show that the mass spectrum of squarks and sleptons carries the information on the breaking pattern of the gauge symmetry. It is demonstrated in some SO(10) models how the scalar mass spectrum distinguishes various SO(10) breaking patterns from each other.

String unification and threshold corrections

The interpretation of the apparent unification of gauge couplings within supersymmetric theories depends on uncertainties induced through heavy particle thresholds. While in standard grand unified theories these effects can be estimated easily, the corresponding calculations are quite complicated in string unified theories and do exist only in models with unbroken E 6. We present results for heavy particle thresholds in more realistic models with gauge group SU(3) × SU(2) × U(1). Effects of Wilson line background fields as well as the universal part of the (rather mild) threshold corrections indicate a strong model dependence. We discuss the consequences of our results for the idea of string unification without a grand unified gauge group.

Sparticle masses as a probe of gut physics

We show that the spontaneous breaking of intermediate-scale gauge symmetries at scale M I or M GUT) ⪢ m W induced by soft supersymmetry-breaking terms μ 1 2 , m 0, A ⋍ O(m W ) causes sizable D-term contributions O( m W) to all low-energy scalar masses (squarks, sleptons and higgses) which possess non-vanishing charges under the broken generators. Using this fact one can discriminate, based on the low-energy spectrum, between various popular intermediate-scale or grand-unified gauge groups. We prescribe a corrected procedure for computing large logarithmic corrections to the low-energy potential which includes leading logarithms generally neglected in previous calculations.

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.

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.

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.

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.