The Coleman-Weinberg mechanism in early cosmology

The SU(5) → SU(3) × SU(2) × U(1) phase transition is examined in the case of zero Higgs bare mass. We find that, depending on assumptions made, two scenarios are most likely to occur. Either the transition is rapidly completed into the SU(3) × SU(2) × U(1) phase, or the Universe supercools down to temperatures where the theory gets strongly coupled. In the latter case non-perturbative effects come into play.     

Phase Structures of U(l) and SU(2) Lattice Gauge Models at Finite Temperature

With the variational-cumulant expansion (VCE) method, the phase structures of the U(1) and SU(2) lattice gauge models at finite temperature are studied. The order parameter Polyakov line with N_T = 2 is calculated to the fourth order. For the U(1) and SU(2) lattice gauge models in D = 3 + 1 and D = 2 + 1 at finite temperature, the results show the existence of the second order phase transition.     

The bose form of two-dimensional quantum chromodynamics

By means of a special choice of gauge QCD₂ [SU(N)] with one flavor of quarks is recast into the Bose form. Weak (g m) and strong (gm) coupling regimes are studied. The former is shown to be the SU(N)-symmetric confining phase in which bound states possess stringlike configurations with strings being represented by electric vortex lines; the ordinary mesons and baryons appear as longitudinal modes of electric strings. The strong coupling regime describes the Higgs phase with the residual symmetry [U(1)]^N−1 S_N where the left and right factors are the maximal abelian subgroup of SU(N) and the permutation group of N quarks, respectively; the particle spectrum consists of S_N multiplets and the [Uw(1)]^N−1 charges are trapped.     

The mass-scale of supersymmetry breaking and proton decay

A fundamental mass-scale is associated with the transition of supersymmetric SU(3)_c×SU(2)_L×U(1) to the ordinary SU(3)_c×SU(2)_L×U(1) symmetry of elementary particle interactions. The renormalisation of the gauge coupling in a supersymmetric SU(5) grand unification leads to the mass-scale of supersymmetry breaking to be of order 10¹² GeV if the lifetime of the proton is taken to be 10³⁰ y and is lowered to the mass-scale of ordinary electroweak interactions if the proton lives longer than 10³⁰ y. It is lower than 10¹² GeV if the contribution of light scalars is taken into account. The predictions of the weak angle sin²θ (M_W) are in excellent agreement with experiment.     

Effects of additional Higgs doublets on the Coleman-Weinberg SU(2) × U(1) → U(1)em phase transition

In the standard electroweak theory with a Coleman-Weinberg Higgs doublet, it has been shown that the SU(2) × U(1) → U(1)_em phase transition is driven by chiral symmetry breaking and that a phenomenologically dangerous amount of entropy is produced. We show that the addition of a second, sufficiently heavy Coleman-Weinberg doublet will make the transition go via tunneling and will suppress excessive entropy generation.     

Roughening transition in lattice gauge theories in arbitrary dimension: (II). The groups Z3, U(1), SU(2), SU(3)

Strong coupling expansions for the string tension and other quantities in lattice gauge theories are computed in arbitrary dimension for the groups Z₃, U(1), SU(2), SU(3). This enables us to determine the location of the roughening transition, which seems to be group independent when measured in an appropriate variable. In four dimensions, the strong coupling expansion of string tension calculated up to fourteenth order for SU(2), and twelfth order for SU(3) agrees nicely with Monte Carlo data up to the roughening point.     

Higgs fields and the determination of the Weinberg angle

SU(2) × U(1) gauge theories, in which the Higgs fields transform as doublets under SU(2) are interpreted as pure Yang-Mills theories in six dimensions, the components of the gauge potentials in the extra dimensions playing the role of the Higgs' fields. Two consistent theories are discovered: one in which SU(2) × U(1) is embedded in SU(3) and the vector bosons remain massless - and another where SU(2) × U(1) is embedded in the graded Lie algebra SU(2|1), the symmetry is spontaneously broken in a natural fashion and the theory is equivalent to that of Weinberg and Salam, with a specific value 30° for the Weinberg angle and a prediction of the Higgs' mass.     

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.     

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)′.     

ELECTRO-WEAK UNIFIED TNEQRY AND RELATED PROBLEMS

The minimum SU(2)×U(1) electro-weak unified theory is described and several related problems including the connection between anomaly free and charge quantization, Kobayashi-Maskawa mixing and CP violation and Higgs sector are dis-cussed. The experimental verification minimum of SU(2)×U(1) model in low energy range is presented briefly. Physical conseguences concerning to free W and Z particles are discussed. The possibilities of the existence or gauge symmetry higher than SU(2)×U(1) for electro-weak interaction and with the minimum SU(2)×U(1) model as the first order of approximation in the low energy range are given. New phenomena involving Z Partice and their implication based on SU(2)×U(1) model are examined.     

The phase structure of mixed lattice gauge theories

The mixed compact-non-compact U(1) model is shown to be equivalent to a compact U(1) Higgs model. It is argued that the mixed SO(3)-SU(2) model is dual to an SO(3) gauge theory coupled to a scalar field in the fundamental representation. The degrees of freedom are Z(2) monopoles and charges or, in a dual picture, monopoles and loops. This picture is supported by a Monte Carlo calculation. The implications for the SU(2) transition region are discussed.     

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.     

An invisible axion with a single Higgs isodoublet

We propose an SU(3) SU(2) U(1) gauge model with an invisible axion and a single Higgs isodoublet. The main peculiarity of the model is the use of non-renormalizable effective interactions left over from whatever theory combines SU(3) SU(2) U(1) with gravity. We also discuss the SU(5) extensions of the proposed model.     

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.     

Phase transitions and magnetic monopoles in SO(10)

In a unified gauge theory based on SO(10), the combination of a strongly first order phase transition and a magnetic confinement mechanism can suppress the density of magnetic monopoles at the time of nucleosynthesis. However, this only occurs if SO(10) breaks down to SU(3)_c ? U (1)_em via SU(4)_c ? [SU(2)_L × SU(2)_R]. For the other symmetry breaking patterns of SO(10) obtained with a minimal Higgs system, the potential conflict with the standard big bang cosmology is not naturally avoided.     

Radiative corrections to quark-lepton mass matrices in superstring-inspired models

We examine if quark-lepton mass matrices are modified by generation changing currents in superstring-inspired models. It is shown that sufficiently large corrections to the quark mass matrices can be derived in an SU(3)_C × SU(2)_L × SU(2)_R × U(1)_L × U(1)_R model with δ ⩾ 2 and an SU(3)_C × SU(2)_L × U(1)_L × U(1)_R model. Consistency with other experiments are investigated by means of renormalization group equations.     

An orbifold compactification with three families from twisted sectors

We obtain a three generational SU(3)_c×SU(3)_w×U(1)⁴×[SO(12)×U(1)²]′ model from an orbifold construction with the requirement that three generations arise from twisted sectors. There exist supersymmetric vacua realizing the standard model. In one example the anomalous U(1) breaks the gauge symmetry down to SU(3)_c×SU(3)_w×U(1)_y×SO(12)′.     

142-164Dy核的低能谱和电磁跃迁的相互作用玻色子模型

采用IBM模型研究了^142-164Dy核的低能正宇称态的能谱和电磁跃迁。应用U(5)→SU(3)的简化哈密顿量较好地描述了它们的能谱和电磁跃迁。研究结果表明，该核基本属于U(5)→SU(3)的过渡核Spectra and E2 transition rates for the even even 142-164Dy isotopes are studied in the framework of the interacting boson model. A schematic Hamiltonian capable of describing their spectra and transition is used. It is found that the even even 142-164Dy isotopes are in the transition from U(5)to SU(3) dynamical symmetry.     

FINITE TEMPERATURE EFFECTIVE POTENTIAL AND COSMOLOGICAL INFLATION IN WEINBERG-SALAM MODEL

The finite temperature effective potential in SUSY Weinberg-Salam model, proposed by Sohnius, is calculated. The temperature of the phase transition is found approximately. The scale of this temperature is of the order of hiqqs mass, it is the same as that in standard model. There is no influence on the phase transition from the Slavnov term. The cosmological inflationt SU(2)×U(1)epoch in such a model is estimated.     

SU(3) ⊗ SU(2) ⊗ U(1) from D = 11 supergravity

In this paper we show that D = 11 supergravity admits an infinite discrete class of solutions having the phenomenological group SU(3) ? SU(2) ? U(1) as a symmetry of the internal space M₇. These solutions lead, in dimensional reduction, to SU(3) ? SU(2) ? U(1) gauge fields.In general all these spaces produce a complete breaking of supersymmetry except in one case where N = 2 supersymmetry survives. The parameter which classifies the solutions is a rational number q/p which describes the embedding of the stability subgroup SU(2) ? U(1) ? U(1) of M₇ in SU(3) ? SU(2) ? U(1). For all q/p ≠ 1 the holonomy group is SO(7) and all supersymmetries are broken. For q/p = 1 the holonomy group is SU(3) and two supersymmetries survive. In this last case we can also find a solution with internal photon curl $\text{F}{}_{\mathrm{\alpha \beta \gamma \delta }}\text{≠ 0}$. It breaks all sypersymmetries.