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.     

Phase structure of the SU(5) Coleman-Weinberg theory

The phase structure of the SU(5) Coleman-Weinberg theory in the one-loop approximation is obtained with account of temperature and space-time curvature. We show that the most essential contribution is that from the interaction between 5 and 24 scalar fields which reflects the existence of two strongly different mass scales in the model. A stability boundary of the SU(3) × SU(2) × U(1) phase is found. It is shown that the SU(4) × U(1) phase in the Coleman-Weinberg theory is unstable.     

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.     

Baryon number generation in a flipped SU(5) × U(1) model

We consider the possibilities for generating a baryon asymmetry in the early universe in a flipped SU(5) × U(1) model inspired by the superstring. Depending on the temperature of the radiation background after inflation we can distinguish between two scenarios for baryogenesis: (1) after reheating the original SU(5) × U(1) symmetry is restored, or there was no inflation at all; (2) reheating after inflation is rather weak and SU(5) × U(1) is broken. In either case the asymmetry is generated by the out-of-equilibrium decays of a massive SU(3) × SU(2) × U(1) singlet field φ_m. In the flipped SU(5) × U(1) model, gauge symmetry breaking is triggered by strong coupling phenomena, and is in general accompanied by the production of entropy. We examine constraints on the reheating temperature and the strong coupling scale in each of the scenarios.     

含G对费米子动力学对称SP(10)模型的Dyson玻色子实现

将费米子动力学对称模型包含G费米子对能够构造出SP(10)或SO(12)动力学对称群.本文用GeneralizedDyson玻色子映射方法求出SP(10)对称群精确的玻色子映像,其子群SU(5)生成元的玻色子映像与sdg相互作用玻色子模型(IBM)SU(5)生成元相同,唯象sdgIBMSU(5)极限能谱公式可由费米子动力学对称模型的微观参数描述.     

将超对称大统一理论嵌入扩充超引力的尝试

本文假设N=8扩充超引力能形成复合超多重态,并探讨了{3/2,8}_N=8^SU(8)和{2,28}_N=8^SU(8)两种复合超多重态容纳SU(5)超对称大统一理论的可能性。在较为苛刻的假设下,能由{3/2,8}_N=8^SU(8)方案得到三代轻子夸克和较满意的SU(5)超对称大统一粒子谱。在较为合理的假设下,能由{2,28}_N=8^SU(8) 关键词：     

A classification of compactifying solutions for d =11 supergravity

Supergravity in eleven dimensions is known to have classical solutions of the type (anti-de Sitter space-time) × (7-dimensional Einstein space). We give a list of all homogeneous 7-manifolds which admit an Einstein metric. Known solutions are reviewed, with some emphasis on the SU(3) × SU(2) × U(1) compactifications. Their topology is discussed in detail.The list includes three new solutions, with symmetry groups SU(3) × SU(2), SO(5) and SO(5) × U(1). The first solution has no supersymmetry, while the second and third yield respectively N = 1 and N = 2 supersymmetry in four dimensions. The last two solutions may be extended to solutions with nonzero internal photon curl, breaking all supersymmetry.The existence of a spin structure on homogeneous manifolds $\text{G}\text{H}$ is discussed and related to topological properties of $\text{G}\text{H}$. As an illustration, we treat the coset spaces SU(m + 1) × SU(n + 1)/SU(m) × SU(n) × U(1), which include the spaces with SU(3) × SU(2) × U(1) symmetry.     

Economic models for Dirac neutrinos in grand unified theories

It is shown that dimension five non-renormalizable interactions can produce light Dirac neutrinos in an extension of the minimal SU(5) GUT containing additional SU(5) singlets and global U(1) symmetries.     

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.     

Monte Carlo studies of SU(N)/ZN lattice gauge theories in four dimensions

Using Monte Carlo techniques on a four-dimensional space-time lattice, we study SU(N)/Z_N gauge theories for N = 3, 4, 5 and 6. We find first-order phase transitions at critical inverse temperatures of β_c = 6.40, 12.0, 19.5 and 32.0 and SU(3)/Z₃,SU(4)/Z₄,SU(5)/Z₅and SU (6)Z₆, respectively.     

Nonabelian electric and magnetic flux in unified SU(5) gauge theory

We study the long-distance behaviour of pure unified SU(5) gauge theory in the limit when the electroweak subgroup is unbroken. We show that the symmetry breaking pattern SU(5)→SU(3)_c×SU(2)×U(1)_Y, with SU(3)_c and SU(2) ×U(1)_Y realized, respectively, in confining and coulombic phases, is a possible dynamical phase of the SU(5) theory. The proof relies on showing that the duality equation of 't Hooft, relating the electric and magnetic flux, is exactly satisfied for the above symmetry breaking pattern. The infrared structure of SU(5), broken down to SU(3)_c×SU(2)×U(1)_Y, is not self-dual.     

Anti-Su(5)

We discuss ordinary as well as supersymmetric SU(5) ×?(1) models in the hope of accomodating acceptable τ_p and sin²θ_W. The ordinary SU(5) ×?(1) model does not have the monopole. The supersymmetric SU(5) ×?(1) model can be unified in SO(10).     

SU(5) monopoles,magnetic symmetry and confinement

The monopoles of the unified SU(5) gauge theory broken down to H_E = SU(3)_c ? U(1)_EM [or to K_E = SU(3)_c ? SU(2) ? U(1)_Y], are classified. They belong to representations of a magnetic group H_M(K_M), which is found to be isomorphic to H_E(K_E). For SU(5) broken down to H_E, there exists a regular and stable monopole which is a colour magnetic triplet, and carries a non-zero abelian magnetic charge. It is suggested that composite operators made out of this monopole and its antiparticle fields develop a non-zero vacuum expectation value, and so lead to a squeezing of the colour electric flux. Finally, we comment on the cosmological production of SU(5) monopoles.     

Topology of the Symmetry Group of the Standard Model

We study the topological structure of thesymmetry group of the standard model, G_SM =U(1) × SU(2) × SU(3). Locally,G_SM S¹ ×(S3)² × S⁵. For SU(3), whichis an S³-bundle over S⁵ (and therefore a local product of thesespheres) we give a canonical gauge i.e., a canonical setof local trivializations. These formulas give explicitlythe matrices of SU(3) without using the Lie algebra (Gell-Mann matrices). Globally, we prove thatthe characteristic function of SU(3) is the suspensionof the Hopf map . We also study the case of SU(n) forarbitrary n, in particular the cases of SU(4), a flavor group, and of SU(5),a candidate group for grand unification. We show thatthe 2-sphere is also related to the fundamentalsymmetries of nature due to its relation to SO⁰(3, 1), the identity component of the Lorentz group, asubgroup of the symmetry group of several gauge theoriesof gravity.     

More flipped SU(5)×U(1) baryosynthesis

We supplement a previous discussion of baryosynthesis in flipped SU(5)×U(1) GUTs by including (1) the large incoherent field energy density which is likely SU(5) is broken, and (2) the possibility of additional Higgs triplet fields suggested by four dimensional string model-building. We consider strong (weak) reheating scenarios in which the Universe is (is not) SU(5) symmetric after inflation. We find an adequate baryon asymmetry subsequent to strong reheating, whatever the number of Higgs triplets (although beware of possible difficulties with quasi-stable relic particles), whereas weak reheating requires at least two Higgs triplets.     

Spontaneous symmetry breaking in O(10)

We consider the most general renormalizable O(10) invariant potential for a $\text{45 + 16 +}\text{16}$ representation of Higgs fields. We show that O(10) can be spontaneously broken down to SU(5), SU(4) × U(1) or SU(3) × SU(2) × U(1), this last case being, of course, the most appealing.     

Triplication of SU(5) Monopoles

We investigate all spherically symmetric fundamental monopole solutions with fixed topological charge in the SU(5)-->[SU(3) x SU(2) x U(1)]/Z(3) x Z(2) symmetry breaking. We find that there are three solutions that are gauge equivalent but, as we argue, would correspond to physically distinct degrees of freedom in the dualized version of the model. The triplication of monopoles could help us understand the observed family structure of standard model particles.     

The SU(8) GUT for chiral families

We argue that there is a natural inclusion of the standard model with the family-unified chiral local symmetry SU(3)_H in a new SU(8) GUT inspired by Georgi's SU(11) model. The SU(8) symmetry breaking along the chain with the intermediate electro-weak-horizontal unification SU(8)→SU(5)_EWH×SU(3)_c×U(1) is proved d to be the distinguished pattern. The model predicts a long-lived proton (10³³–10³⁵yr) and practically the observed value of the Weinberg angle, in sharp contrast to the ordinary GUTs. The observation of the specific flavour-changing baryon decays (p→π,μ,Ke,…) could unambiguously single out the flavour unified GUTs as well as confirm the existence of the elementary horizontal forces at small distances.     

Absolute proton stability in unified models of strong,weak and electromagnetic interactions

We show that the proton can be made absolutely stable, without introducing superheavy bosons, by imposing a global U(1) color symmetry on the Higgs couplings of the theory. Vector-like SU(5) and SU(6) models are discussed in detail.     

Multi-component fractional quantum Hall states in graphene: SU(4) versus SU(2)

Because of the spin and Dirac-valley degrees of freedom, graphene allows the observation of one-, two- or four-component fractional quantum Hall effects in different parameter regions. We address the stability of various states in the SU(2) and SU(4) limits. In the SU(4) limit, we predict that new low-energy Goldstone modes determine the stability of the fractional quantum Hall states at 2/5, 3/7, etc; SU(4) skyrmions are not found to be relevant for the low-energy physics. These results are discussed in light of experiments.