Group theoretic dimension of stationary symmetric \alpha-stable random fields

The growth rate of the partial maximum of a stationary stable process was first studied in the works of Samorodnitsky (2004a,b), where it was established, based on the seminal works of Rosi\'nski (1995,2000), that the growth rate is connected to the ergodic theoretic properties of the flow that generates the process. The results were generalized to the case of stable random fields indexed by Z^d in Roy and Samorodnitsky (2008), where properties of the group of nonsingular transformations generating the stable process were studied as an attempt to understand the growth rate of the partial maximum process. This work generalizes this connection between stable random fields and group theory to the continuous parameter case, that is, to the fields indexed by R^d.Comment: To appear in Journal of Theoretical Probability. Affiliation of the authors are update

Variant supercurrent multiplets

In N = 1 rigid supersymmetric theories, there exist three standard realizations of the supercurrent multiplet corresponding to the (i) old minimal, (ii) new minimal and (iii) non-minimal off-shell formulations for N = 1 supergravity. Recently, Komargodski and Seiberg in arXiv:1002.2228 put forward a new supercurrent and proved its consistency, although in the past it was believed not to exist. In this paper, three new variant supercurrent multiplets are proposed. Implications for supergravity-matter systems are discussed.Comment: 11 pages; V2: minor changes in sect. 3; V3: published version; V4: typos in eq. (2.3) corrected; V5: comments and references adde

Higher Spin Gauge Theory and Holography: The Three-Point Functions

In this paper we calculate the tree level three-point functions of Vasiliev's higher spin gauge theory in AdS4 and find agreement with the correlators of the free field theory of N massless scalars in three dimensions in the O(N) singlet sector. This provides substantial evidence that Vasiliev theory is dual to the free field theory, thus verifying a conjecture of Klebanov and Polyakov. We also find agreement with the critical O(N) vector model, when the bulk scalar field is subject to the alternative boundary condition such that its dual operator has classical dimension 2.Comment: 90 pages, 5 figures; v4, minor changes in the introductio

Variant supercurrents and Noether procedure

Consistent supercurrent multiplets are naturally associated with linearized off-shell supergravity models. In arXiv:1002.4932 we presented the hierarchy of such supercurrents which correspond to all the models for linearized 4D N = 1 supergravity classified a few years ago. Here we analyze the correspondence between the most general supercurrent given in arXiv:1002.4932 and the one obtained eight years ago in hep-th/0110131 using the superfield Noether procedure. We apply the Noether procedure to the general N = 1 supersymmetric nonlinear sigma-model and show that it naturally leads to the so-called S-multiplet, revitalized in arXiv:1002.2228.Comment: 6 page

Taming the Runaway Problem of Inflationary Landscapes

A wide variety of vacua, and their cosmological realization, may provide an explanation for the apparently anthropic choices of some parameters of particle physics and cosmology. If the probability on various parameters is weighted by volume, a flat potential for slow-roll inflation is also naturally understood, since the flatter the potential the larger the volume of the sub-universe. However, such inflationary landscapes have a serious problem, predicting an environment that makes it exponentially hard for observers to exist and giving an exponentially small probability for a moderate universe like ours. A general solution to this problem is proposed, and is illustrated in the context of inflaton decay and leptogenesis, leading to an upper bound on the reheating temperature in our sub-universe. In a particular scenario of chaotic inflation and non-thermal leptogenesis, predictions can be made for the size of CP violating phases, the rate of neutrinoless double beta decay and, in the case of theories with gauge-mediated weak scale supersymmetry, for the fundamental scale of supersymmetry breaking.Comment: 31 pages, including 3 figure

Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions

Large enhancement of the thermopower in Nax_xCoO2_2 at high Na doping

Research on the oxide perovskites has uncovered electronic properties that are strikingly enhanced compared with those in conventional metals. Examples are the high critical temperatures of the cuprate superconductors and the colossal magnetoresistance in the manganites. The conducting layered cobaltate $\rm Na_xCoO_2$ displays several interesting electronic phases as $x$ is varied including water-induced superconductivity and an insulating state that is destroyed by field. Initial measurements showed that, in the as-grown composition, $\rm Na_xCoO_2$ displays moderately large thermopower $S$ and conductivity $\sigma$. However, the prospects for thermoelectric cooling applications faded when the figure of merit $Z$ was found to be small at this composition (0.6$<x<$0.7). Here we report that, in the poorly-explored high-doping region $x>$0.75, $S$ undergoes an even steeper enhancement. At the critical doping $x_p\sim$ 0.85, $Z$ (at 80 K) reaches values $\sim$40 times larger than in the as-grown crystals. We discuss prospects for low-temperature thermoelectric applications.Comment: 6 pages, 7 figure

Lifetimes of image-potential states on copper surfaces

The lifetime of image states, which represent a key quantity to probe the coupling of surface electronic states with the solid substrate, have been recently determined for quantum numbers $n\le 6$ on Cu(100) by using time-resolved two-photon photoemission in combination with the coherent excitation of several states (U. H\"ofer et al, Science 277, 1480 (1997)). We here report theoretical investigations of the lifetime of image states on copper surfaces. We evaluate the lifetimes from the knowledge of the self-energy of the excited quasiparticle, which we compute within the GW approximation of many-body theory. Single-particle wave functions are obtained by solving the Schr\"odinger equation with a realistic one-dimensional model potential, and the screened interaction is evaluated in the random-phase approximation (RPA). Our results are in good agreement with the experimentally determined decay times.Comment: 4 pages, 1 figure, to appear in Phys. Rev. Let

Estimating the nuclear level density with the Monte Carlo shell model

A method for making realistic estimates of the density of levels in even-even nuclei is presented making use of the Monte Carlo shell model (MCSM). The procedure follows three basic steps: (1) computation of the thermal energy with the MCSM, (2) evaluation of the partition function by integrating the thermal energy, and (3) evaluating the level density by performing the inverse Laplace transform of the partition function using Maximum Entropy reconstruction techniques. It is found that results obtained with schematic interactions, which do not have a sign problem in the MCSM, compare well with realistic shell-model interactions provided an important isospin dependence is accounted for.Comment: 14 pages, 3 postscript figures. Latex with RevTex. Submitted as a rapid communication to Phys. Rev.