Grand unified theories in coset space dimensional reduction

We examine particle content of the effective four-dimensional GUT's arising in the coset space dimensional reduction of 10-dimensionalE ₈ supersymmetric Yang-Mills theory.     

Grand unified theory precursors and nontrivial fixed points in higher-dimensional gauge theories

Within the context of traditional logarithmic grand unification at M(GUT) approximately equal to 10(16) GeV, we show that it is nevertheless possible to observe certain GUT states such as X and Y gauge bosons at lower scales, perhaps even in the TeV range. We refer to such states as "GUT precursors." These states offer an interesting alternative possibility for new physics at the TeV scale, and could be used to directly probe GUT physics even though the scale of gauge coupling unification remains high. Our results also give rise to a Kaluza-Klein realization of nontrivial fixed points in higher-dimensional gauge theories.     

Grand unified theories in the framework of the SU(N) group

Due to the problem of flavour, the general SU(N) gauge group is considered as a candidate for grand unification. Starting from a set of general requirements, we find restrictions and conditions for the construction of grand unified theories within the framework of such a group. The allowed groups get restricted to SU(6), SU(7) and SU(8).     

Hierarchical models of unified theories

A modernized conception of hierarchical structure of reality is proposed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 3–6, December, 1980.     

New challenges in unified theories

Among the research directions that we have presented during the Workshop SQS??2011, we have chosen to discuss here in some detail the derivation of the effective action in four dimensions of the tendimensional N = 1 heterotic supergravity coupled to N = 1 supersymmetric Yang-Mills resulting from the dimensional reduction over nearly-K?hler manifolds.     

Grand unified models including extraZ bosons

The grand unified theories (GUT) of the simple Lie groups including extraZ bosons are discussed. There are onlySU _5+m,SO _6+4n, andE ₆ under our hypothesis. First we give a general discussion forSU _5+m, then forSU ₆ andSU ₇ for illustration. We use15 +6 ^* +6 ^* fermion representations inSU ₆ but not with the fermion content, Yukawa coupling, and the hierarchy of other authors. We suggest that there is a series of clans of particles. These clans consist of the extraZ bosons and the corresponding fermions of the scale.     

Grand unified strings and galaxy formation

The possibility that topologically stable strings formed at a grand unification phase transition led to galaxy formation is discussed. A large class of solutions describing non-self-intersecting loops is presented. The gravitational field and power radiated from a simple class of oscillating configurations of string is calculated, and the possibility of its detection discussed. Unique features of the string scenario are emphasized.     

Grand unified schemes and spontaneous compactification

The mass spectrum of spontaneously compactified Einstein-Yang-Mills theories is computed using the Wu-Yang monopole harmonic functions. It is found that spontaneous compactification can be used to provide the correct mass scale generating the superstrong symmetry breaking which, in grand unified theories, separates quarks from leptons.     

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.     

Low-energy predictions from grand unified theories

A theoretical framework to compute low-energy processes in a spontaneously broken gauge theory is devised. It applies in any gauge and uses conventional renormalisation schemes. Application of the method to SU(5) gives a range for M_X of 4.10¹³ GeV < M_X < 1.3 · 10¹⁵ GeV with a best value of 6.6 · 10¹⁴ GeV.     

Grand unification of effective gauge theories

An effective non-renormalizable SU(3)×SU(2)×U(1) invariant gauge theory results at ordinary energies when superheavy fields are integrated out from a grand unified theory based on a simple gauge group G. The solutions of the second-order renormalization-group equations for the gauge coupling constants of the effective theory are examined. General formulae for the superheavy vector boson mass and for sin²θ near M_W are given in this approach to grand unification. The superheavy vector boson mass is plotted against the QCD scale parameter Λ for a certain set of grand unified models. Corrections to the prediction when the set of models is enlarged are discussed, and illustrated with examples from G≡SU(5) and O(10).     

LEP constraints on grand unified theories

Recent developments on grand unified theories (GUTs) in the context of the LEP measurements of the coupling constants will be reviewed. The three coupling constants at the electroweak scale have been measured at LEP quite precisely. One can allow these couplings to evolve with energy following the renormalization group equations for the various groups and find out whether all the coupling constants meet at any energy. It was pointed out that the minimalSU (5) grand unified theory fails to satisfy this test. However, various extensions of the theory are still allowed. These extensions include (i) supersymmetricSU (5) GUT, with some arbitrariness in the susy breaking scale arising from the threshold corrections, (ii) non-susySU (5) GUTs with additional fermions as well as Higgs multiplets, which has masses of the order of TeV, and (iii) non-renormalizable effect of gravity with a fine tuned relation among the coupling constants at the unification energy. The LEP results also constrain GUTs with an intermediate symmetry breaking scale. By adjusting the intermediate symmetry breaking scale, one usually can have unification, but these theories get constrained. For example, the left-right symmetric theories coming from GUTs can be broken only at energies higher than about ～ 10¹⁰ GeV. This implies that if right handed gauge bosons are found at energies lower than this scale, then that will rule out the possibility of grand unification. Another recent interesting development on the subject, namely, low energy unification, will be discussed in this context. All the coupling constants are unified at energies of the order of ～ 10⁸ GeV when they are embedded in anSU (15) GUT, with some particular symmetry breaking pattern. But even in this case the results of the intermediate symmetry breaking scale remain unchanged.     

Finite unified theories and their predicitions

All-loop Finite Unified Theories (FUTs) are very interesting N = 1 supersymmetric Grand Unified Theories (GUTs) realising an old field theory dream, and moreover have a remarkable predictive power due to the required reduction of couplings. The reduction of the dimensionless couplings in N = 1 GUTs is achieved by searching for renormalization group invariant (RGI) relations among them holding beyond the unification scale. Finiteness results from the fact that there exist RGI relations among dimensional couplings that guarantee the vanishing of all beta-functions in certain N = 1 GUTs even to all orders. Additional developments in the soft supersymmetry breaking sector of N = 1 GUTs and FUTs lead to exact RGI relations, i.e. reduction of couplings, in this dimensionful sector of the theory, too. Based on the above theoretical framework phenomenologically consistent FUTs have been constructed. Here we review two FUT models based on the SU(5) gauge group. Confronting their predictions with the top and bottom quark masses and other experimental constraints a light Higgs-boson mass in the range M _H ～ 121–126 GeV has been predicted, in striking agreement with the recent experimental results from ATLAS and CMS. Furthermore naturally a relatively heavy s-spectrum emerged with coloured supersymmetric particles above ～1.5 TeV in agreement with the non-observation of those particles at the LHC. Restricting further the parameter space of the best version of the SU(5) FUT according to the reported accuracy of the Higgs boson mass and B-physics observables we find predictions for the rest of the Higgs masses and the s-spectrum.     

Quantized Grassmann variables and unified theories

The color and flavor degrees of freedom are described in terms of Fermi oscillators (quantized Grassmann variables). The unified theories constructed in this way are vector-like. The fundamental fermions come out to be classified in the spinorial representations of the orthogonal groups.     

Supersymmetric grand unified theories and the early universe

Consequences of supersymmetric, grand unified theories (with supersymmetry unnbroken at the tree level) for the production of baryons and magnetic monopoles in the early universe are discussed.