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.     

Branes, geometry and N = 1 duality with product gauge groups of SO and Sp

We study N = 1 dualities in four-dimensional supersymmetric gauge theories as the world volume theory of D4 branes with one compact direction in type IIA string theory. We generalize the previous work for SO(N_c1) × Sp(N_c2) with the superpotential W = TrX⁴ to the case of W = TrX^4(k+1) in terms of brane configuration. We conjecture that the new dualities for the product gauge groups of SO(N_c1) × Sp(N_c2) × SO(N_c3), SO(N_c1) × Sp(N_c2) × SO(N_c3) × Sp(N_c4) and higher multiple product gauge groups can be obtained by reversing the ordering of NS5 branes and D6 branes while preserving the linking numbers. We also describe the above dualities in terms of wrapping D6 branes around 3-cycles of Calabi-Yau threefolds in type IIA string theory. The theory with adjoint matter can be regarded as taking multiple copies of NS5 brane in the configuration of brane or geometric approaches.     

The mesoscopic and microscopic structural consequences from decomposition and desorption of ultrathin oxide layers on Si(100) studied by scanning tunneling microscopy

The spatially inhomogeneous decomposition and desorption reaction of oxide layers with coverage 1-0.3 monolayers (ML) from a silicon (100) surface has been studied using scanning tunneling microscopy (STM). After desorption, microscopic changes to the (2 × 1) reconstruction produce two variations on the dimer row reconstruction with decreased surface atom density. A (2 × n) vacancy chain reconstruction and a c(4 × 4) incomplete row reconstruction were observed; a structure for the latter is proposed. Both reconstructions are metastable, reforming the (2 × 1) reconstruction upon heating. At greater length scales during desorption from an initial 1.0 ML coverage, the mesoscopic changes to the surface structure include pitting and roughening, with up to a measured 20 fold increase in the edge density as compared to the clean Si(100) surface.

These structural changes suggest a reaction mechanism involving a substantial rearrangement of the substrate silicon. From an initial 1.0 ML oxygen coverage, using measured void size distributions at total desorption levels of 13% and below — before voids have begun to coalesce — the evolution of void sizes during initial desorption can be followed. A mechanism for desorption is proposed in which silicon atoms must diffuse from adjacent clean surface area to the oxide boundary, producing a reactive complex from which SiO is desorbed. Void growth rates derived from two rate limiting cases for this desorption reaction mechanism can be compared to measured results. We show that the measured void area evolution is consistent with a reaction mechanism where the rate limiting step for monolayer desorption is the promotion of a silicon atom in a lattice site to a mobile monomer within the void.     

Electron microscopy study on microstructures of infinite-layer compound Sr0.86Nd0.14CuO2

The infinite-layer compound with nominal composition of Sr_0.86Nd_0.14CuO₂ synthesized under high pressure has been investigated by high-resolution transmission microscopy as well as selected area electron diffraction techniques. The microtwin originating from the tetragonal-orthorhombic phase transformation and the 2×b superstructure are observed in such an infinite-layer compound for the first time. The n×c (n=2, 3, 4, …) superstructures and their origin are discussed. Computer image simulation reveals that the 2×c superstructure is due to the oxygen deficiency.     

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.     

Quenched master field equations for unitary matrix models

We derive the quenched master field equations for constrained systems such as the O(N) non-linear sigma model, U(N)×U(N) chiral models, and U(N) lattice gauge theory. The master equations are algebraic, and involve quenching in both the space and “fifth” (Langevin) time directions. The quenched master field for the O(N) nonlinear sigma model is found exactly. The 0-dimensional unitary matrix model is solved perturbatively, and we recover the Gross-Witten result. The master equation for the U(N)×U(N) chiral model is set up for non-perturbative approximation methods, and some qualitative results are obtained.     

The reaction of H2S with surface oxygen on Ni(110)

The reactions of H₂S with predosed surface oxygen on Ni(110) surfaces were studied for a variety of coverage conditions. The primary reaction product is H₂O, but the details of the water formation and desorption depends on the coverage of both O and H₂S.

For high coverages of oxygen (p(2 × 1)−O; 0.5 ML), the reaction to form water is quantitative. The loss of oxygen from the surface (as measured by AES) is equal to the increase in sulfur coverage. XPS and HREELS measurements indicate the presence of chemisorbed H₂O immediately following large exposures of H₂S on the oxygen predosed surface at 110 K. Deuterium incorporation results suggest that the primary mechanism for these coverage conditions involves direct transfer of hydrogen from SH or H₂S moieties to the oxygen.

A second mechanism involving reaction of surface hydroxyl groups with surface hydrogen was also identified. This mechanism is particularly important for high coverages of oxygen (0.5 ML) and low coverages of H₂S (0.15 ML), where water desorption was observed at 235 K, but was not observed spectroscopically at 110 K. The sequential addition of two surface hydrogen atoms to surface oxygen is not an important mechanism in this system.

These reactions were modeled using a bond-order conservation method, and the model successfully reproduced the important mechanistic conclusions.     

Does the quenched reduced U(∞) chiral model break spontaneously in weak coupling?

The U(N) chiral model, when quenched using Parisi's rule, has a [U(1) × U(1)]^N/U(1) global invariance. To determine whether this symmetry breaks spontaneously in weak coupling for N=∞, a one-loop calculation of the distribution of eigenvalues of the single U(N) matrix of the model is performed. This distribution is shown to be uniform on the unit circle and hence, no symmetry breaking occurs. Further, the order parameter | tr U|²/N², which should be zero at N=∞ in the absence of spontaneous symmetry breaking, is evaluated in the weak coupling phase for one, two and three dimensions for N varying from 2 to 50 by Monte Carlo simulation of the quenched model. The data indicate that this parameter indeed goes to zero as N→∞ implying that the symmetry does not break.     

Yang–Lee zeros of the Ising model on random graphs of non planar topology

We obtain in a closed form the 1/N² contribution to the free energy of the two Hermitian N×N random matrix model with nonsymmetric quartic potential. From this result, we calculate numerically the Yang–Lee zeros of the 2D Ising model on dynamical random graphs with the topology of a torus up to n=16 vertices. They are found to be located on the unit circle on the complex fugacity plane. In order to include contributions of even higher topologies we calculated analytically the nonperturbative (sum over all genus) partition function of the model for the special cases of N=1,2 and graphs with n≤20 vertices. Once again the Yang–Lee zeros are shown numerically to lie on the unit circle on the complex fugacity plane. Our results thus generalize previous numerical results on random graphs by going beyond the planar approximation and strongly indicate that there might be a generalization of the Lee–Yang circle theorem for dynamical random graphs.     

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.     

RNA folding and large N matrix theory

We formulate the RNA folding problem as an N×N matrix field theory. This matrix formalism allows us to give a systematic classification of the terms in the partition function according to their topological character. The theory is set up in such a way that the limit N→∞ yields the so-called secondary structure (Hartree theory). Tertiary structure and pseudo-knots are obtained by calculating the 1/N² corrections to the partition function. We propose a generalization of the Hartree recursion relation to generate the tertiary structure.     

ESDIAD studies of the structure of TiO2(110)(1 × 1) and (1 × 2) surfaces and interfaces in conjunction with LEED and STM

The TiO₂(110)-(1 × 1) surface and its reconstruction as a (1 × 2) form have been studied with low energy electron diffraction (LEED), electron stimulated desorption ion angular distribution (ESDIAD) and scanning tunnelling microscopy (STM). Oxygen ion desorption occurs within a lobe perpendicular to the (1 × 1) surface, changing to two off-normal lobes for the (1 × 2) reconstruction. This transformation in the ESDIAD pattern is consistent with the added Ti₂O₃ row model of the (1 × 2) reconstruction proposed by Onishi and Iwasawa. STM studies of the stoichiometric and electron irradiated surfaces reinforce the association of the O⁺ ESD contribution with majority sites at the surface. Adsorption of acetic acid on the (1 × 1) surface produces a (2 × 1) overlayed and induces a reconstruction of the underlying substrate. ESDIAD reveals H⁺ ions emitted off-normally from dissociatively adsorbed acetate, and along the surface normal from surface hydroxyls. Adsorption of acetic acid on the (1 × 2) surface does not modify the LEED pattern, but ESDIAD reveals H⁺ desorption with a weaker off-normal contribution consistent with the Ti₂O₃ model of the reconstruction.     

Universal ZN-graded differential calculus

We investigate the propeties of differential algebras generated by an operator d satisfying the property d^N = 0 instead of d² = 0 as in the usual case. Several examples of realizations of such differential algebras are given, either in the context of Z_N-graded N × N matrix algebras, or as a generalized differential calculus on manifolds.     

The study of hydronium NASICON conductivity with deuterium

The ionic conductivity of the bulk phase of bonded hydronium NASICON (Hyceram^TM) was measured at equilibrium with an H₂O/N₂ and then a D₂O/N₂ atmosphere, each at 100% relative humidity and 75% relative humidity over the temperature range 25°C to 50°C. At 100% relative humidity and 25°C, the protonic system had a bulk conductivity of 5.0×10⁻⁴ S/cm and an activation energy of 17.3kJ/mole; the same sample, when deuterated, had a bulk conductivity of 2.2×10⁻⁴ S/cm and an activation energy of 19.3kJ/mole. At 75% relative humidity and 25°C, the conductivity of the protonated system decreased to 1.4×10⁻⁴S/cm with an activation energy of 24.1 kJ/mole. The deuterated sample at 75% relative humidity had a bulk conductivity of 5.4×10⁻⁵ S/cm with an activation energy of 26.0 kJ/mole. The isotope effect suggested a proton hopping (Grotthus) mechanism as the means by which the protons pass through the lattice.     

Motion of Chern-Simons number at high temperatures under a chemical potential

I investigate the evolution of finite temperature, classical Yang-Mills field equations under the influence of a chemical potential for Chern-Simons number N_cs. The rate of N_cs diffusion,, Γ_d, and the linear response of N_cs to a chemical potential, Γ_μ, are both computed; the relation Γ_d = 2Γ_μ is satisfied numerically and the results agree with the recent measurement of Γ_d by Ambjørn and Krasnitz. The response of N_cs under chemical potential remains linear at least to μ = 6T, which is impossible if there is a free energy barrier to the motion of N_cs. The possibility that the result depends on lattice artefacts via hard thermal loops is investigated by changing the lattice action and by examining elongated rectangular lattices; provided that the lattice is fine enough, the result is weakly if at all dependent on the specifics of the cutoff. I also compare SU(2) with SU(3) and find Γ_SU(3) 7(_{s/w)⁴ΓSU(2)}.     

Rotational epitaxy of a hexagonal layered material on a square substrate: PbI2 on InSb(001)

PbI₂ has been adsorbed on the clean InSb(001)-(4 × 1) reconstructed surface and on the InSb(001)-(1 × 3)-Pb lead covered reconstructed surface. On the clean surface epitaxial growth occurred with the unit mesh of the layered PbI₂ aligning exactly with both the substrate [110] and [1 0] directions. On desorption a reaction occurred between the last layer of PbI₂, and the substrate, forming a series of structures which finished with a well-formed (1 × 3)-Pb structure in which the surface is depleted/enriched in In/Sb compared to the clean (4 × 1). The Pb in this structure is thought to partially replace surface In. Epitaxial adsorption also occurred on the (1 × 3)-Pb surface generating a single, well-formed structure with the hexagonal net of the PbI₂ aligned with just the [1 0] substrate direction. The structures and reactions are discussed and a row matching model is proposed to explain the single epitaxial orientation of PbI₂ on the (1 × 3)-Pb surface.     

Electron stimulated desorption of CO from Pd1/W(110)

The electron impact behavior of CO adsorbed on Pd₁/W(110) was investigated. The desorption products observed were neutral CO, CO⁺, and O⁺. After massive electron impact residual carbon, C/W = 0.15, but not oxygen was also found, suggesting that energetic neutral O, not detected in a mass analyzer must also have been formed. Formation of β-CO, i.e., dissociated CO with C and O on the surface was not seen. The total disappearance cross section varies only slightly with coverage, ranging from 9 × 10 ⁻¹⁸ cm² at low to 5 × 10⁻¹⁸ cm² at saturation (CO/W = 0.75). The cross section for CO⁺ formation varies from 4 × 10⁻²² cm² at satura to 2 × 10⁻²¹ cm² at low coverage. That for O⁺ formation is 1.4 × 10⁻²² cm² at saturation and 2 × 10⁻²¹ cm² Threshold energies are similar to those found previously [J.C. Lin and R. Gomer, Surf. Sci. 218 (1989) 406] for CO/W(110) and CO/Cu₁/W(110) which suggests similar mechanisms for product formation, with the exception of β-CO on clean W(110). It is argued that the absence or presence of β-CO in ESD hinges on its formation or absence in thermal desorption, since electron impact is likely to present the surface with vibrationally and rotationally activated CO in all cases; β-CO formation only occurs on surfaces which can dissociate such CO. It was also found that ESD of CO led to a work function increase of the remaining Pd₁/W(110) surface of 500 meV, which could be annealed out only at 900 K. This is attributed to surface roughness, caused by recoil momentum of energetic desorbing entities.     

Surface reconstructions of the Si(100)–Ge system

The surface reconstruction of epitaxial Ge layer on Si(100) was studied with ultrahigh vacuum scanning tunneling microscopy. The surface with 0.8 ML Ge grown in the presence of a hydrogen surfactant reveals the same structures as found in chemical-vapor-deposited Ge on Si(100): (i) defective (2×1) structure at 290°C, (ii) irregular (2×N) in Ge layer and defective (2×1) in bare Si regions at 420°C, and (iii) (2×N) in Ge-covered regions and c(4×4) in bare Si regions at 570°C. The morphology of step edges does not change with temperature, implying that the c(4×4) reconstruction is anisotropic in nature.     

LEED studies of the adsorption of CO2 on thin epitaxial NaCl(100) films

The adsorption of CO₂ on the NaCl(100) surface was studied with a high-resolution LEED-system. Measurements without charging up at low electron energies and without damage by the e-beam could be performed by using ultrathin epitaxial films on a conducting Ge(100) substrate. The adsorption behavior was recorded as a function of time and pressure at constant substrate temperatures of 78 and 83 K and CO₂ partial pressures from 4 × 10⁻⁸−2 × 10⁻³ Pa. The adsorption system shows a first-order two-dimensional phase transition to a (2 × 1) superstructure including glide planes (herringbone-like structure) at p = 7.2 × 10⁻⁸Pa (T = 78 K). The condensation of the CO₂ solid is starting at p = 1.5 × 10⁻⁴ Pa (T = 78 K). The LEED-pattern shows in this c(2 × 2) superstructure, which corresponds to the pyrite-like structure of the CO₂ solid. Both observed superstructures are commensurable with the NaCl(100) surface. Observation of island growth shows that the domains of the (2 × 1) superstructures have already at coverage of 5% of a monolayer an average lateral size of at least 200 A.