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.     

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.     

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.     

Orbifolded SU(7) and unification of families

A 5D SU(7) family unification model with two spinor representations of SO(14) is presented. The fifth dimension is compactified on S¹/Z₂×Z₂′. The orbifolding is used to obtain 4D SO(10) chiral fermions. The 4D grand unification group is the flipped SU(5)×U(1). The doublet–triplet splitting through the missing partner mechanism is achieved. Also, fermion mass matrices are considered.     

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.     

Family unification, exotic states and magnetic monopoles

The embedding in SU(4)×SU(3)×SU(3) of the well studied gauge groups SU(4)×SU(2)×SU(2) and SU(3)×SU(3)×SU(3) naturally leads to family unification as opposed to simple family replication. An inescapable consequence is the predicted existence of (exotic) color singlet states that carry fractional electric charge. The corresponding magnetic monopoles carry multiple Dirac magnetic charge, can be relatively light (10⁷–10¹³ GeV), and may be present in the galaxy not far below the Parker bound.     

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.     

In-band M1 and E2 transition rates and collective structures in Ba

Subpicosecond mean lifetimes of eight excited states in ¹²⁸Ba populated via the ⁹⁶Zr(³⁶S,4n) reaction were measured by the Doppler-shift attenuation (DSA) technique using a line-shape analysis. The differential decay-curve method (DDCM) was applied for the lifetime determination. The B(E2) values in the yrast band indicate that the first band-crossing is with a proton S-band. The configuration πh_11/2d_5/2 of the negative-parity semi-decoupled bands is confirmed by the measured B(E2, I → I − 2) and B(M1, I → I − 1) transition strengths. The higher-lying “dipole” band in ¹²⁸Ba can be described as a high-K four-quasiparticle band built on the prolate configuration (πh_11/2d_5/2) (νh_11/2g_7/2).     

A simple theoretical treatment of quadrupolar effects on magic-angle-spinning solid-state NMR spectra of spin-1/2 nuclei in the limit of large quadrupole coupling constants

A simple approach is discussed for studying the effect of quadrupolar nuclei on the magic-angle-spinning solid-state NMR lines of spin-1/2 nuclei in the limit of large quadrupole coupling constants. Equations are derived both for the isotropic shifts and the Pake-like powder patterns for any quadrupolar spin and for arbitrary orientations of the internuclear vector with respect to the unique axis of an axially symmetric quadrupole tensor. First-order effects due to a small Zeeman perturbation on these lines are explored, as well as deviations from axial symmetry in the electric field gradient when S = 3/2 quadrupolar nuclei are involved. Spectral parameters likely to be observed in the case of coupling between ³¹P and ²⁰¹Hg are also discussed.     

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.     

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.     

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.     

The geometry of the SU(2) Kepler problem

The SU(2) Kepler problem is defined and analyzed, which is a Hamiltonian system reduced from the conformal Kepler problem on T^*( ⁸ − {0}) by the use of the symplectic SU(2) action lifted from the SU(2) left action on the SU(2) bundle ⁸ − {0} → ⁵ − {0}. This reduced system has a parameter μ ε su(2) coming from the value of the moment map associated with the symplectic SU(2) action. If μ ≠ 0, the phase space of this system have a bundle structure with base space T^*( ⁵ − {0}) and fibre S². The fibre, a (co)adjoint orbit through μ for SU(2), represents the internal degrees of freedom, called the isospin, of the particle of this system. The SU(2) Kepler problem with μ ≠ 0 is then interpreted as describing the motion of a classical particle with isospin in the Newtonian potential plus a specific repulsive potential together with a Yang-Mills field. This Yang-Mills field is to be referred to as BPST Yang's monopole field in ⁵ − {0};, since it becomes the Belavin-Polyakov-Schwartz-Tyupkin instanton, restricted on S⁴. If μ = 0, the SU(2) Kepler problem reduces to the ordinary Kepler problem. Like the ordinary Kepler problem, the Hamiltonian flows of the SU(2) Kepler problem of negative energy are all closed. It is shown in an explicit manner that the energy manifolds and isoenergetic orbit spaces for the SU(2) Kepler problem of negative energy are both homogeneous manifolds on which SU(4) acts transitively to the right; those homogeneous manifold are classified into two, according as the parameter μ is zero or not. For a certain value of μ, however, they contracts to the manifold which represents the set of all the equilibrium states. The isoenergetic orbit spaces are finally shown to be symplectomorphic to certain Kirillov-Konstant-Souriau coadjoint orbits for U(4), if μ is not the exceptional value mentioned above.     

Cranked Skyrme–Hartree–Fock calculation for superdeformed and hyperdeformed rotational bands in N=Z nuclei from S to Cr

With the use of the symmetry-unrestricted cranked Skyrme–Hartree–Fock method in the three-dimensional coordinate-mesh representation, we have carried out a systematic theoretical search for the superdeformed and hyperdeformed rotational bands in the mass A=30–50 region. Along the N=Z line, we have found superdeformed solutions in ³²S, ³⁶Ar, ⁴⁰Ca, ⁴⁴Ti, and hyperdeformed solutions in ³⁶Ar, ⁴⁰Ca, ⁴⁴Ti, ⁴⁸Cr. The superdeformed band in ⁴⁰Ca is found to be extremely soft against both the axially symmetric (Y₃₀) and asymmetric (Y₃₁) octupole deformations. An interesting role of symmetry breaking in the mean field is pointed out.     

High-resolution solid state 13C nuclear magnetic resonance spectra of 3,4-methylenedioxyamphetamine hydrochloride and related compounds and their mixtures with lactose

Differences between solution and solid state ¹³C nuclear magnetic resonance spectra of some amphetamines namely, 3,4-methylenedioxyamphetamine·HCl, (R,S)-MDA·HCl, the methyl derivative 3,4-methylenedioxy-N-methylamphetamine·HCl, (R,S)-MDMA·HCl, the ethyl derivative, (R,S)-MDEA·HCl, and the analogues (R,S)-methamphetamine·HCl, (−)-ephedrine·HCl (the 3R,2S enantiomer as numbered here), and (+)-pseudo-ephedrine·HCl (the 3S,2S enantiomer as numbered here) have been studied and related to their crystal structure. For (R,S)-MDMA·HCl, an interesting new finding is that the observed solid state chemical shifts changed when lactose monohydrate was added as a dry powder and thoroughly mixed at room temperature. This experiment mimicked the illicit production of “Ecstasy” tablets. The mixing phenomena with lactose observed for (R,S)-MDMA·HCl was not seen for the other compounds studied. The results are discussed in terms of hydrogen bonding and possible polymorphs. It appears that lactose affects crystal packing by reducing conformational rigidity so that the molecule more closely resembles that in solution.     

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     

Quasi-exactly solvable decatic model description of nuclei near the X(5) critical point

The Bohr Hamiltonian with axially deformed shape confined in a quasi-exactly solvable decatic β-part potential is studied.It is shown that the decatic model can well reproduce the X(5)model results as far as the energy ratios in the ground and beta band and related B(E2)values are concerned.Fitting results to the low-lying energy ratios and relevant B(E2)values of even-even X(5)candidates ¹⁵⁰Nd,¹⁵⁶Dy,¹⁶⁴Yb,¹⁶⁸Hf,¹⁷⁴Yb,^176,178,180Os,and ^188,190Os show that the decatic model provides the best fitting results for the energy ratios,while the X(5)model is the best at reproducing the B(E2)values of these nuclei,in which the beta-bandhead energy is lower than that of the gamma band.While for even-even nuclei,such as ^154,156,158Gd,with bandhead energies of the beta and gamma bands more or less equal within the X(5)critical point to the axially deformed region,our numerical analysis indicates that the decatic model is better than the X(5)model in describing both the low-lying level energies and related B(E2)values.     

Spectral intensities in the ν1 band of NH3

Intensities have been measured for individual transitions in the Q and R branches of the ν₁ band of NH₃ using a difference-frequency laser spectrometer. The data yield an integrated band strength of S⁰_v=219.36±1.03 cm^-2/MPa at 297 K, corresponding to a transition moment of μ_v = 8.535(20) × 10^-32 C·m, and a Herman-Wallis correction factor, (1 + _jm)², where _j = 0.0209(20). The intensities of a few lines for K 7 were noticeably perturbed by a perpendicular Coriolis interaction with 2ν₄ (E, L = 2), so were excluded from the fit. A small sample of ν₃ band lines occurring in the ν₁ band scans also yields a rough estimate of the ν₃ band intensity with evident irregular perturbations.