A study of SU(3) × SU(2) × U(1) × U(1) as an intermediate energy subgroup of SO(10)

We analyze several patterns of symmetry breaking of SO(10) where SU(3)_c × SU(2) × U(1) × U(1) is an intermediate energy subgroup. Using constraints from the renormalization group and data from neutral-current experiments we show that if the only Higgs used in the low-energy breaking of the theory are those which can give mass to fermions then the possibility of a low intermediate mass scale is ruled out.     

Breaking of the SO(n) symmetry with vector and adjoint higgses

The spontaneous symmetry breaking of SO(n) is investigated by studying the most general quartic SO(n)-invariant Higgs potential with two multiplets of scalars belonging to a vector and to an adjoint representation. In the most general cases largest residual symmetry is found to be SU(l), SU(l-1), SO(l), SO(l-1) or SO(n-2) wherel is the rank of SO(n). In particular, the breaking of SO(n) into SU(n ₁)×SU(n ₂) is found to occur only in special cases.     

Possible symmetry breaking patterns with totally symmetric and antisymmetric representations

Possible symmetry breaking patterns for SU(N) gauge theories with Higgs scalars in totally antisymmetric and symmetric representations of degree k are discussed by solving the extremum conditions.     

SU(5) Higgs problem with adjoint + vector representations

Recently Kim has given a general method, using group-invariant orbit parameters, for determining the energy and residual symmetry of the Higgs potential minimum. In this paper we illustrate the method by working out the case of a quartic SU(5) Higgs potential with $\text{5}$ and $\text{24}$ higgsons. In this method the Gell-Mann-Slansky conjecture concerning possible little groups of the potential minimum takes a geometric form, which is verified for our case. The results are used to discuss the hierarchical symmetry breaking of SU(5) grand unification theory. We generalize our results to the SU(N) adjoint + vector models, which are all closely related.     

Complementarity in preon models with E6 metacolor

Tumbling complementarity is studied in chiral preon models based on the metacolor group E₆. By considering the breaking of E₆ into each maximal little group in the Higgs phase, several models are found that are in accord with complementarity. Three families of massless fermions (on the metacolor scale) can be obtained, but so far we have been unable to identify an E₆ × SU(N) preon model supported by complementarity that correctly predicts the quantum numbers of ordinary quarks and leptons.     

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.     

Topology of quantum gauge fields and duality (I): Yang-Mills-Higgs system in 2 + 1 dimensions

The basic role of the representation of the gauge group in characterizing the topological excitations of the vacuum is pointed out. For SU(N) gauge fields on a lattice, the topological excitations are monopoles in the adjoint representation of the dual group ¹SU(N). This leads to a dual representation of the Yang-Mills-Higgs system in 2 + 1 dimensions. For SU(3) the deal theory in a scalar theory with discrete Weyl symmetry S₃. In the presence of adjoint Higgs fields the Weyl symmetry is broken in the Higgs phase but restored by pseudo-particles in the confinement phase.     

Masses and Mixing of Neutral Leptons in a Grand Unified <Emphasis Type="Italic">E</Emphasis><Subscript>6</Subscript> Model with Intermediate Pati-Salam Symmetry

A brief review of the assignment of elementary fermions and bosons to irreducible multiplets in grand unified \(E_{6}\) models is followed by a discussion of different, hierarchical symmetry breaking chains from \(E_{6}\) down to \(SU(3)_{C} \times U(1)_{EM}\). We concentrate here on a model with an intermediate Pati-Salam symmetry for which \((B-L)\) is conserved. In particular, the mass/mixing matrix of electrically neutral fermions (i.e.neutrinos) that would be derived from Yukawa couplings is constructed. The pattern of neutrino masses and some bounds on mixing parameters are discussed.     

Instantons and the U(1) problem

If instantons spontaneously break the chiral SU(N) × SU(N) symmetry of a non-abelian gauge theory, they break U(1) symmetry in a manner consistent with the chiral Ward identities of the theory. Excitations of the fermion vacuum play a crucial role in this process. A model calculation of the symmetry breaking effect shows a phenomenological structure which differs from that provided by models with many color degrees of freedom.     

Possibility of a doubly-charged structure at theS-meson mass

The various symmetry breaking patterns that are possible with a 24-plet and a 5-plet of Higgs fields in SU(5) are classified. Spontaneous breakdown of SU(5) to SU(3)_colour×U(1) _em can be achieved (excluding the gauge hierarchy problem) without imposing unnatural constraints on the parameters of the Higgs potential.     

Discrete symmetries in SO(N) grand unified groups and the survival hypothesis

The possibility of introducing the discrete symmetry D is studied, which along with SU^c(3) × SU_L(2) × U(1)-symmetry, remains after the breaking of SO(N) grand unified symmetry by the Higgs fields vevs ～ 10¹⁵ GeV. The D quantum number distinguishes the fermions coupled with W-bosons via left and right currents. As a result, the presence of low-mass fermions in the theory is provided.     

Fat branes,orbifolds and doublet-triplet splitting

A simple higher dimensional mechanism of the doublet-triplet splitting is presented in a five dimensional supersymmetric SU(5) GUT on S¹/Z₂. The splitting of multiplets is realized by a mass term of the Higgs hypermultiplet which explicitly breaks SU(5) gauge symmetry. Depending on the sign of the mass, zero mode Higgs doublets and triplets are localized on either side of the fixed points. The mass splitting is realized due to the difference of magnitudes of the overlap with a brane localized or a bulk singlet field. No unnatural fine-tuning of the parameters is needed. The proton stability is ensured by locality - without symmetries.Received: 17 September 2003, Revised: 21 November 2003, Published online: 4 February 2004Nobuhito Maru: Special Postdoctoral Researcher     

Left-right symmetry breaking scale and supersymmetry in unified theories

We propose a class of supersymmetric grand unified models where parity and SU(2)_R breaking scales are widely separated and compatible with a low-lying mass for the right-handed gauge boson W_R. The intermediate symmetry SU(4)_c×SU(2)_L×SU(2)_R and Higgs content are uniquely fixed if m_WR < 10⁹ GeV. The unification scale lies within an order of magnitude below the Planck mass.     

SU (8) mass relations amongJ P=1/2+ and 3/2+ baryons

Mass relations among charmed and uncharmed baryons belonging to20 and20′ multiplets of SU(4) are derived in the framework of SU(8) symmetry, Spin singlet mass breaking interaction is found to give unsatisfactory results. Second order effects and spin triplet mass breaking interactions are studied to improve the situation.     

Continuum symmetries of lattice models with staggered fermions

The validity of the flavour interpretation of staggered fermions is discussed in terms of the discrete symmetries of the interaction terms. Some aspects of the embedding of these symmetries in the symmetry group of the continuum limit are clarified. An explicit calculation, at first non-trivial order in 1/N, of the four-point function for a latticized Gross-Neveu model yields the same result in the continuum limit as the continuum theory for 2N fermions. A proof is then given that flavour and C, P, and T symmetries are restored in the continuum limit of 2-point correlation functions, for interactions, including the case of 4-dimensional QCD, which respect the discrete symmetries of the free action.     

A low right-handed scale in a supersymmetric context

We investigate the prospects for a low right-handed scale M_R in the context of locally supersymmetric O(10), limiting ourselves to the most interesting case of a single breaking scale between the grand unified scale M_X and the W-mass. It is found that supersymmetry seems to imply a unique solution as regards the Higgs content and the intermediate symmetry group if a low right-handed scale (less than 10⁴ GeV) exist at all. Apart from a minimal set of representations providing the symmetry battern, the Higgs sector consist of a pair of 16 and $\text{16}$ spinor representations ying at scale M_R and the residual symmetry is SU(3)_c × U(1)_B?L × SU(2)_L × U(1)_R.     

The complete N = 3 matter coupled supergravity

The complete N = 3 matter coupling to supergravity is obtained in a geometrical framework. This coupling always exists if the 3n complex scalars of the n vector multiplets are co-ordinates of the Kähler-grassmannian manifold SU(3, n)/SU(3) × SU(n) × U(1). Subgroups of SO(3, n) ⊂ SU(3, n) of dimension 3 + n can be gauged and give rise to a non-trivial scalar potential. The techniques used in this paper allow for the calculation of scalar potentials of extended supergravities in any dimension without explicit construction of the lagrangian. This opens the possibility of discussing patterns of partial supersymmetry and gauge symmetry breaking on a purely group-theoretical ground.     

Effect of the renormalization group on the symmetry breaking patterns of SU(n) Higgs potentials

As a first step toward the study of the effects of radiative corrections on spontaneously broken potentials we consider the renormalization group equations for those parameters which determine the shape of the potential and the symmetry breaking patterns. As examples we consider the Higgs potential for a single scalar field and for the adjoint represention of SU(n). In the latter case we also obtain some results at the classical level - a new proof of the Michel conjecture, the Higgs mass spectrum and an explicit expression for the parameter that determines the symmetry breaking pattern.     

Symmetry-breaking scenarios of Wilson-loop broken E6

In superstring theories formulated on a multiply-connected manifold, E₆ gauge symmetry can be broken at the Planck scale to an extended standard model via an effective Higgs adjoint. It is possible to arrange for the coloured components of a Higgs 27 to gain a large mass via this Wilson-Loop breaking while leaving some colour singlet components massless. The remaining light Higgs representations can then be applied to break the extended electroweak symmetry at a lower scale. We investigate some of the symmetry-breaking scenarios for a rank-six extended group. We find that the Higgs multiplets left light after Wilson-loop breaking are not sufficient to break the extended electroweak symmetry to U₁^em     

The weak mixing angle and unification mass in supersymmetric SU(5)

We consider the predictions for the weak mixing angle θ_W and the scale M of unification in a supersymmetric extension of SU(5), with particular emphasis on the sensitivity to the number of Higgs multiplets. In the one-loop approximation, we also calculate the ratio m_b/m_τ. We discuss generally the effects of an intermediate threshold between the weak interaction scale and M and estimate the sensitivity of θ_W and M to the scale of supersymmetry breaking.The evolution of the coupling constants of the supersymmetric SU(3) ? SU(2) ? U(1) effective gauge theory is described and the two-loop corrections to θ_{W and M} are calculated.