Specific scalar mass relations in SU(3) × SU(2) × U(1) orbifold model

We study flat directions and soft scalar masses using a Z₃ orbifold model with SU(3) × SU(2) × U(1) gauge group and extra gauge symmetries including an anomalous U(1) symmetry. Soft scalar masses contain D-term contributions and particle mixing effects after symmetry breaking and they are parametrized by a few parameters. Some specific relations among scalar masses are obtained.     

Matter–antimatter asymmetry and neutrino properties

The cosmological baryon asymmetry can be explained as remnant of heavy Majorana neutrino decays in the early universe. We study this mechanism for two models of neutrino masses with a large ν_μ−ν_τ mixing angle which are based on the symmetries SU(5)×U(1)_F and SU(3)_c×SU(3)_L×SU(3)_R×U(1)_F, respectively. In both cases B−L is broken at the unification scale Λ_GUT. The models make different predictions for the baryogenesis temperature and the gravitino abundance.     

N=2 6-dimensional supersymmetric E6 breaking

We study the N=2 supersymmetric E₆ models on the 6-dimensional space–time where the supersymmetry and gauge symmetry can be broken by the discrete symmetry. On the space–time M⁴×S¹/(Z₂×Z₂′)×S¹/(Z₂×Z₂′), for the zero modes, we obtain the 4-dimensional N=1 supersymmetric models with gauge groups SU(3)×SU(2)×SU(2)×U(1)², SU(4)×SU(2)×SU(2)×U(1), and SU(3)×SU(2)×U(1)³ with one extra pair of Higgs doublets from the vector multiplet. In addition, considering that the extra space manifold is the annulus A² and disc D², we list all the constraints on constructing the 4-dimensional N=1 supersymmetric SU(3)×SU(2)×U(1)³ models for the zero modes, and give the simplest model with Z₉ symmetry. We also comment on the extra gauge symmetry breaking and its generalization.     

The spectral density of the QCD Dirac operator and patterns of chiral symmetry breaking

We study the spectrum of the QCD Dirac operator for two colors with fermions in the fundamental representation and for two or more colors with adjoint fermions. For N_f flavors, the chiral flavor symmetry of these theories is spontaneously broken according to SU (2N_f → Sp (2N_f) and SU (N_f → O (N_f), respectively, rather than the symmetry breaking pattern SU (N_f) × SU (N_f) → SU (N_f) for QCD with three or more colors and fundamental fermions. In this paper we study the Dirac spectrum for the first two symmetry breaking patterns. Following previous work for the third case we find the Dirac spectrum in the domain λ Λ_QCD by means of partially quenched chiral perturbation theory. In particular, this result allows us to calculate the slope of the Dirac spectrum at λ = 0. We also show that for λ 1/L₂ Λ_QCD (wing L the linear size fo the system) the Dirac spectrum is given by a chiral Random Matrix Theory with the symmetries of the Dirac operator.     

The top quark mass and flavour mixing in a seesaw model of quark masses

The top quark mass and the flavour mixing are studied in the context of a seesaw model of quark masses based on the gauge group SU(2)_L × SU(2)_R × U(1). Six isosinglet quarks are introduced to give rise to the mass hierarchy of ordinary quarks. In this scheme, we reexamine a mechanism for the generation of the top quark mass. It is shown that, in order to prevent the seesaw mechanism to act for the top quark, the mass parameter of its isosinglet partner must be much smaller than the breaking scale of SU(2)_R. As a result the fourth lightest up quark must have a mass of the order of the breaking scale of SU(2)_R, and a large mixing between the right-handed top quark and its singlet partner occurs. We also show that this mechanism is compatible with the mass spectrum of light quarks and their flavour mixing.     

Gauge-Higgs unification in the left–right model

We construct a supersymmetric left–right model in four dimension with gauge-Higgs unification starting from a SU(3)_c×SU(4)_w×U(1)_B−L gauge symmetry in five dimension. The model has several interesting features, such as, the CKM mixings in the quark sector are naturally small while for the neutrino sector it is not, light neutrino masses can be generated via the seesaw mechanism in the usual way, and the model has a U(1)_R symmetry which naturally forbid dimension five proton decay operators. We also discuss the grand unification of our model in SO(12) in five dimensions.     

Duality and quantum-algebra symmetry of the AN−1 open spin chain with diagonal boundary fields

We show that the transfer matrix of the A_N−1⁽¹⁾ open spin chair with diagonal boundary fields has the symmetry U_q(SU(l)) × U_q(SU(N−l)) × U(1), as well as a “duality” symmetry which maps l ↔ N − l. We exploit these symmetries to compute exact boundary S-matrices in the regime with q real.     

Exact monodromy group of N = 2 heterotic superstring

We describe an N = 2 heterotic superstring model of rank 3 which is dual to the type II string compactified on a Calabi-Yau manifold with Betti numbers b_1,1 = 2 and b_1,2 = 86. We show that the exact duality symmetry found from the type II realization contains the perturbative duality group of the heterotic model, as well as the exact quantum monodromies of the rigid SU(2) super-Yang-Mills theory. Moreover, it contains a non-perturbative monodromy which is stringy in origin and corresponds roughly to an exchange of the string coupling with the compactification radius.     

M-theory on AdS4 × M: the complete Osp(2|4) × SU(3) × SU(2) spectrum from harmonic analysis

We reconsider the Kaluza-Klein compactifications of D = 11 supergravity on AdS₄ × (G/H)₇ manifolds that were classified in the eighties, in the modern perspective of AdS₄/CFT₃ correspondence. We focus on one of the three N = 2 cases: (G/H)₇ = M¹¹¹ = SU(3) × SU(2) × U(1) /SU(2) × U(1)′ × U(1)′'. Relying on the systematic use of the harmonic analysis techniques developed in the eighties by one of us (P. Fré) with R. D'Auria, we derive the complete spectrum of long, short and massless Osp(2|4) × SU(3) × SU(2) unitary irreducible representations obtained in this compactification. Our result also provides a general scheme for the other N = 2 compactifications. Furthermore, it is a necessary comparison term in the AdS₄/CFT₃ correspondence: the complete AdS/CFT match of the spectra that we obtain will provide a much more stringent proof of the ACS/CFT correspondence than in the S⁷ case, since the structure of the superconformal field theory on the M2-brane world volume must be such as to reproduce, at the level of composite operators, the flavor group representations, the conformal dimensions and the hyperchanges that we obtain in the present article. The investigation of this match is left to future publications. Here we provide an exhaustive construction of the Kaluza-Klein side of our spectroscopy.     

Unified models at intermediate energy scales and Kaluza–Klein excitations

We discuss the possibility of intermediate gauge coupling unification in unified models of string origin. Useful relations of the β-function coefficients are derived, which ensure unification of couplings when Kaluza–Klein excitations are included above the compactification scale. We apply this procedure to two models with SU(3)×SU(3)_L×SU(3)_R and SU(4)×O(4) gauge symmetries.     

Quantum group invariant fermionic gases: GLp,q(2) and SUp/q(2) invariances

We first investigate the high-temperature behavior of a two-parameter deformed quantum group fermionic gas with GL_p,q(2) symmetry, where (p,q)C×C. We then discuss both the structural and thermodynamical differences between GL_p,q(2)- and SU_r(2)-fermions with r=p/q where (p,q)R×R.     

Commutator representations of differential calculi on the quantum group SUq(2)

Let (Γ, d) be the 3D-calculus or the 4D_±-calculus on the quantum group SU_q (2). We describe all pairs (π, F) of a ^*-representation π of (SU_q(2)) and of a symmetric operator F on the representation space satisfying a technical condition concerning its domain such that there exist a homomorphism of first order differential calculi which maps dx into the commutator [iF, π(x)] for x ε (SU_q (2)). As an application commutator representations of the two-dimensional left-covariant calculus on Podles quantum 2-sphere S_qc² with c = 0 are given.     

GUT breaking on M×T/(Z2×Z2′)

We construct two SU(5) models on the space–time M⁴×T²/(Z₂×Z₂′) where the gauge and Higgs fields are in the bulk and the Standard Model fermions are on the brane at the fixed point or line. For the zero modes, the SU(5) gauge symmetry is broken down to SU(3)×SU(2)×U(1) due to non-trivial orbifold projection. In particular, if we put the Standard model fermions on the 3-brane at the fixed point in model II, we only have the zero modes and KK modes of the Standard Model gauge fields and two Higgs doublets on the observable 3-brane. So, we can have the low energy unification, and solve the triplet–doublet splitting problem, the gauge hierarchy problem, and the proton decay problem.     

Symmetries and exact solutions of some integrable Haldane-Shastry-like spin chains

Here we construct some integrable Haldane-Shastry (HS) like spin chains, which exhibit multi-parameter deformed or non-standard variants of Y(gl_m) Yangian symmetry. By projecting the eigenstates of Dunkl operators in a suitable way, we also derive a class of exact eigenfunctions for such spin chains and subsequently conjecture that these exact eigenfunctions would lead to the highest weight states (HWS) associated with multi-parameter deformed or non-standard variants of Y(gl_M) Yangian algebra. By using this conjecture, and acting descendent operator on the HWS associated with a non-standard Y(gl₂) Yangian algebra, we are able to find out the complete set of eigenvalues and eigenfunctions for the related HS-like chain. It turns out that some additional energy levels, which are forbidden due to a selection rule in the case of SU(2) HS model, interestingly appear in the spectrum of the above mentioned HS-like spin chain with non-standard Y(gl²) symmetry.     

Effect of bare mass on the Hosotani mechanism

It is pointed out that the existence of bare mass terms for matter fields changes gauge symmetry patterns through the Hosotani mechanism. As a demonstration, we study an SU(2) gauge model with massive adjoint fermions defined on M⁴S¹. It turns out that the vacuum structure changes at certain critical values of mL, where m (L) stands for the bare mass (the circumference of S¹). The gauge symmetry breaking patterns are different from models with massless adjoint fermions. We also consider a supersymmmetric SU(2) gauge model with adjoint hypermultiplets, in which the supersymmetry is broken by bare mass terms for the gaugino and squark fields instead of the Scherk–Schwarz mechanism.     

Prediction of sinθW in a conformal approach to coupling unification

The possibility that nonsupersymmetric conformal field theories softly broken below 100 TeV may provide an alternative to conventional grand unification is explored. We consider a low energy theory presumed to be of this type arising from the type IIB superstring compactified on a AdS₅×S₅/Γ space whose gauge group and the particle content are severely restricted by the compactification process. We present an example of a resulting SU(4)_C×SU(2)_L×SU(2)_R with three generations, which leads to coupling unification and a prediction for sin²θ_W0.227 and other phenomenology generally consistent with observations.     

Instantons and the chiral phase transition

We examine the role of instantons in the zero-temperature chiral phase transition in an SU(N) gauge theory. For a range of N_f (the number of fermion flavors) depending on N, the theory exhibits an infrared fixed point at coupling _*. As N_f decreases, _* increases, and it eventually exceeds a critical value sufficient to trigger chiral symmetry breaking. For the case N = 2, we estimate the critical values of N_f and _* due to instantons by numerically solving a gap equation with an instanton-generated kernel. We find instanton effects of strength comparable to that of gluon exchange.     

182Os 核yrast带相继SU(3)–U(5)–SU(3)结构相变势能曲面的一种可能理解

基于联合实施微观相互作用玻色子模型的最大F旋方案 (sdIBM-F_max)与γ射线能量-自旋曲线 (γ-ray energy over spin curves, E-GOS)方案, 成功描述了¹⁸²Os核yrast带相继的SU(3)–U(5)–SU(3)结构相变, 由于缺少直观解释而显得抽象. 本文借助微观sdIBM-F_max的微观参数与Bohr哈密顿量的势能曲面方程之间存在的泛函关系, 几何地给出了对这种相继相变途径的另外一种可能理解; 并阐述了在完全变形核的高角动量态中, 由于量子效应在高激发态与低激发态之间生成高简并的临界区, 提供了γ振动能量会变得低于转动能量的一个可能途径, 从而实现了SU(3)–U(5)的相变. 关键词： yrast带结构演化 势能曲面 相变临界区 182Os核')" href="#">¹⁸²Os核     

Hyperon beta-decay and axial charges of the lambda in view of strongly distorted baryon wave-functions

Within the collective coordinate approach to chiral soliton models we suggest that breaking of SU(3) flavor symmetry mainly resides in the baryon wave-functions while the charge operators maintain a symmetric structure. Sizable symmetry breaking in the wave-functions is required to reproduce the observed spacing in the spectrum of the  baryons. The matrix elements of the flavor symmetric charge operators nevertheless yield g_A/g_V ratios for hyperon beta-decay which agree with the empirical data approximately as well as the successful F&D parameterization of the Cabibbo scheme. Demanding the strangeness component in the nucleon to vanish in the two flavor limit of the model, determines the structure of the singlet axial charge operator and yields the various quark flavor components of the axial charge of the Λ-hyperon. The suggested picture gains support from calculations in a realistic model using pion and vector meson degrees of freedom to build up the soliton.     

Monopoles, vortices and confinement in SU(3) gauge theory

We compute, in SU(3) pure gauge theory, the vacuum expectation value (VEV) of the operator which creates a Z₃ vortex wrapping the lattice through periodic boundary conditions (dual Polyakov line). The technique used is the same already tested in the SU(2) case. The dual Polyakov line proves to be a good disorder parameter for confinement, and has a similar behaviour to the monopole condensate. The new features which characterise the construction of the disorder operator in SU(3) are emphasised.