F-theory, GUTs, and the Weak Scale

In this paper we study a deformation of gauge mediated supersymmetry breaking in a class of local F-theory GUT models where the scale of supersymmetry breaking determines the value of the mu term. Geometrically correlating these two scales constrains the soft SUSY breaking parameters of the MSSM. In this scenario, the hidden SUSY breaking sector involves an anomalous U(1) Peccei-Quinn symmetry which forbids bare mu and B mu terms. This sector typically breaks supersymmetry at the desired range of energy scales through a simple stringy hybrid of a Fayet and Polonyi model. A variant of the Giudice-Masiero mechanism generates the value mu ~ 10^2 - 10^3 GeV when the hidden sector scale of supersymmetry breaking is F^(1/2) ~ 10^(8.5) GeV. Further, the B mu problem is solved due to the mild hierarchy between the GUT scale and Planck scale. These models relate SUSY breaking with the QCD axion, and solve the strong CP problem through an axion with decay constant f_a ~ M_(GUT) * mu / L, where L ~ 10^5 GeV is the characteristic scale of gaugino mass unification in gauge mediated models, and the ratio \mu / L ~ M_(GUT)/M_(pl) ~ 10^(-3). We find f_a ~ 10^12 GeV, which is near the high end of the phenomenologically viable window. Here, the axino is the goldstino mode which is eaten by the gravitino. The gravitino is the LSP with a mass of about 10^1 - 10^2 MeV, and a bino-like neutralino is (typically) the NLSP with mass of about 10^2 - 10^3 GeV. Compatibility with electroweak symmetry breaking also determines the value of tan(beta) ~ 30 +/- 7.Comment: v3: 94 pages, 9 figures, clarification of Fayet-Polonyi model and instanton corrections to axion potentia

Asymmetry Parameter of the K1(1270,1400)K_{1} (1270, 1400) by Analyzing the B→K1ννˉB\to K_{1}\nu \bar{\nu} Transition Form Factors within QCD

Separating the mixture of the $K_{1}(1270)$ and $K_{1}(1400)$ states, the $B\to K_{1}(1270, 1400)\nu\bar{\nu}$ transition form factors are calculated in the three-point QCD sum rules approach. The longitudinal, transverse and total decay widths as well as the asymmetry parameter, characterizing the polarization of the axial $K_{1}(1270, 1400)$ and the branching ratio for these decays are evaluated.Comment: 25 pages, 3 figures, 3 table

Galerkin FEM for fractional order parabolic equations with initial data in H−s, 0<s≤1H^{-s},~0 < s \le 1

We investigate semi-discrete numerical schemes based on the standard Galerkin and lumped mass Galerkin finite element methods for an initial-boundary value problem for homogeneous fractional diffusion problems with non-smooth initial data. We assume that $\Omega\subset \mathbb{R}^d$, $d=1,2,3$ is a convex polygonal (polyhedral) domain. We theoretically justify optimal order error estimates in $L_2$- and $H^1$-norms for initial data in $H^{-s}(\Omega),~0\le s \le 1$. We confirm our theoretical findings with a number of numerical tests that include initial data $v$ being a Dirac $\delta$-function supported on a $(d-1)$-dimensional manifold.Comment: 13 pages, 3 figure

Exact half-BPS Type IIB interface solutions I: Local solution and supersymmetric Janus

The complete Type IIB supergravity solutions with 16 supersymmetries are obtained on the manifold $AdS_4 \times S^2 \times S^2 \times \Sigma$ with $SO(2,3) \times SO(3) \times SO(3)$ symmetry in terms of two holomorphic functions on a Riemann surface $\Sigma$, which generally has a boundary. This is achieved by reducing the BPS equations using the above symmetry requirements, proving that all solutions of the BPS equations solve the full Type IIB supergravity field equations, mapping the BPS equations onto a new integrable system akin to the Liouville and Sine-Gordon theories, and mapping this integrable system to a linear equation which can be solved exactly. Amongst the infinite class of solutions, a non-singular Janus solution is identified which provides the AdS/CFT dual of the maximally supersymmetric Yang-Mills interface theory discovered recently. The construction of general classes of globally non-singular solutions, including fully back-reacted $AdS_5 \times S^5$ and supersymmetric Janus doped with D5 and/or NS5 branes, is deferred to a companion paper.Comment: LaTeX, 69 pages, 3 figures, v2: references adde

Uniaxial Phase Transition in Si : Ab initio Calculations

Based on a previously proposed thermodynamic analysis, we study the relative stabilities of five Si phases under uniaxial compression using ab initio methods. The five phases are diamond, beta-tin, sh, sc, and hcp structures. The possible phase-transition patterns were investigated by considering the phase transitions between any two chosen phases of the five phases. By analyzing the different conributions to the relative pahse stability, we identified the most important factors in reducing the phase-transition pressures at uniaxial compression. We also show that it is possible to have phase transitions occur only when the phases are under uniaxial compression, in spite of no phase transition when under hydrostatic commpression. Taking all five phases into consideration, the phase diagram at uniaxial compression was constructed for pressures under 20 GPa. The stable phases were found to be diamond, beta-tin and sh structures, i.e. the same as those when under hydrostatic condition. According to the phase diagram, direct phase transition from the diamond to the sh phase is possible if the applied uniaxial pressures, on increasing, satisfy the condition of Px>Pz. Simiilarly, the sh-to-beta-tin transition on increeasing pressures is also possible if the applied uniaxial pressures are varied from the condition of Px>Pz, on which the phase of sh is stable, to that of Px<Pz, on which the beta-tin is stable

Hard-core Yukawa model for two-dimensional charge stabilized colloids

The hyper-netted chain (HNC) and Percus-Yevick (PY) approximations are used to study the phase diagram of a simple hard-core Yukawa model of charge-stabilized colloidal particles in a two-dimensional system. We calculate the static structure factor and the pair distribution function over a wide range of parameters. Using the statics correlation functions we present an estimate for the liquid-solid phase diagram for the wide range of the parameters.Comment: 7 pages, 9figure

Threshold criterion for wetting at the triple point

Grand canonical simulations are used to calculate adsorption isotherms of various classical gases on alkali metal and Mg surfaces. Ab initio adsorption potentials and Lennard-Jones gas-gas interactions are used. Depending on the system, the resulting behavior can be nonwetting for all temperatures studied, complete wetting, or (in the intermediate case) exhibit a wetting transition. An unusual variety of wetting transitions at the triple point is found in the case of a specific adsorption potential of intermediate strength. The general threshold for wetting near the triple point is found to be close to that predicted with a heuristic model of Cheng et al. This same conclusion was drawn in a recent experimental and simulation study of Ar on CO_2 by Mistura et al. These results imply that a dimensionless wetting parameter w is useful for predicting whether wetting behavior is present at and above the triple temperature. The nonwetting/wetting crossover value found here is w circa 3.3.Comment: 15 pages, 8 figure

From Finite to Infinite Range Order via Annealing: The Causal Architecture of Deformation Faulting in Annealed Close-Packed Crystals

We analyze solid-state phase transformations that occur in zinc-sulfide crystals during annealing using a random deformation-faulting mechanism with a very simple interaction between adjacent close-packed double layers. We show that, through annealing, infinite-range structures emerge from initially short-range crystal order. That is, widely separated layers carry structurally significant information and so layer stacking cannot be completely described by any finite-range Markov process. We compare our results to two experimental diffraction spectra, finding excellent agreement.Comment: 7 pages, 6 figures; See http://www.santafe.edu/projects/CompMech/papers/iro.htm

Renormalization group study of interacting electrons

The renormalization-group (RG) approach proposed earlier by Shankar for interacting spinless fermions at $T=0$ is extended to the case of non-zero temperature and spin. We study a model with $SU(N)$-invariant short-range effective interaction and rotationally invariant Fermi surface in two and three dimensions. We show that the Landau interaction function of the Fermi liquid, constructed from the bare parameters of the low-energy effective action, is RG invariant. On the other hand, the physical forward scattering vertex is found as a stable fixed point of the RG flow. We demonstrate that in $d=2$ and 3, the RG approach to this model is equivalent to Landau's mean-field treatment of the Fermi liquid. We discuss subtleties associated with the symmetry properties of the scattering amplitude, the Landau function and the low-energy effective action. Applying the RG to response functions, we find the compressibility and the spin susceptibility as fixed points.Comment: 11 pages, RevTeX 3.0, 2 PostScript figure

Understorey plant community and light availability in conifer plantations and natural hardwood forests in Taiwan

Questions: What are the effects of replacing mixed species natural forests with Cryptomeria japonica plantations on understorey plant functional and species diversity? What is the role of the understorey light environment in determining understorey diversity and community in the two types of forest? Location: Subtropical northeast Taiwan. Methods: We examined light environments using hemispherical photography, and diversity and composition of understorey plants of a 35‐yr C. japonica plantation and an adjacent natural hardwood forest. Results: Understorey plant species richness was similar in the two forests, but the communities were different; only 18 of the 91 recorded understorey plant species occurred in both forests. Relative abundance of plants among different functional groups differed between the two forests. Relative numbers of shade‐tolerant and shade‐intolerant seedling individuals were also different between the two forest types with only one shade‐intolerant seedling in the plantation compared to 23 seedlings belonging to two species in the natural forest. In the natural forest 11 species of tree seedling were found, while in the plantation only five were found, and the seedling density was only one third of that in the natural forest. Across plots in both forests, understorey plant richness and diversity were negatively correlated with direct sunlight but not indirect sunlight, possibly because direct light plays a more important role in understorey plant growth. Conclusions: We report lower species and functional diversity and higher light availability in a natural hardwood forest than an adjacent 30‐yr C. japonica plantation, possibly due to the increased dominance of shade‐intolerant species associated with higher light availability. To maintain plant diversity, management efforts must be made to prevent localized losses of shade‐adapted understorey plants