Holographic renormalisation group flows and renormalisation from a Wilsonian perspective

From the Wilsonian point of view, renormalisable theories are understood as submanifolds in theory space emanating from a particular fixed point under renormalisation group evolution. We show how this picture precisely applies to their gravity duals. We investigate the Hamilton-Jacobi equation satisfied by the Wilson action and find the corresponding fixed points and their eigendeformations, which have a diagonal evolution close to the fixed points. The relevant eigendeformations are used to construct renormalised theories. We explore the relation of this formalism with holographic renormalisation. We also discuss different renormalisation schemes and show that the solutions to the gravity equations of motion can be used as renormalised couplings that parametrise the renormalised theories. This provides a transparent connection between holographic renormalisation group flows in the Wilsonian and non-Wilsonian approaches. The general results are illustrated by explicit calculations in an interacting scalar theory in AdS space.Comment: 63 pages. Minor changes and references added. Matches JHEP versio

Ion yields and erosion rates for Si1−xGex(0x1) ultralow energy O2+ secondary ion mass spectrometry in the energy range of 0.25–1 keV

We report the SIMS parameters required for the quantitative analysis of Si1−xGex across the range of 0 ≤ x ≤ 1 when using low energy O2+ primary ions at normal incidence. These include the silicon and germanium secondary ion yield [i.e., the measured ion signal (ions/s)] and erosion rate [i.e., the speed at which the material sputters (nm/min)] as a function of x. We show that the ratio Rx of erosion rates, Si1−xGex/Si, at a given x is almost independent of beam energy, implying that the properties of the altered layer are dominated by the interaction of oxygen with silicon. Rx shows an exponential dependence on x. Unsurprisingly, the silicon and germanium secondary ion yields are found to depart somewhat from proportionality to (1−x) and x, respectively, although an approximate linear relationship could be used for quantification across around 30% of the range of x (i.e., a reference material containing Ge fraction x would give reasonably accurate quantification across the range of ±0.15x). Direct comparison of the useful (ion) yields [i.e., the ratio of ion yield to the total number of atoms sputtered for a particular species (ions/atom)] and the sputter yields [i.e., the total number of atoms sputtered per incident primary ion (atoms/ions)] reveals a moderate matrix effect where the former decrease monotonically with increasing x except at the lowest beam energy investigated (250 eV). Here, the useful yield of Ge is found to be invariant with x. At 250 eV, the germanium ion and sputter yields are proportional to x for all x

Adaptive Optics Observations of the Galactic Center Young Stars

Adaptive Optics observations have dramatically improved the quality and versatility of high angular resolution measurements of the center of our Galaxy. In this paper, we quantify the quality of our Adaptive Optics observations and report on the astrometric precision for the young stellar population that appears to reside in a stellar disk structure in the central parsec. We show that with our improved astrometry and a 16 year baseline, including 10 years of speckle and 6 years of laser guide star AO imaging, we reliably detect accelerations in the plane of the sky as small as 70 microarcsec/yr/yr (~2.5 km/s/yr) and out to a projected radius from the supermassive black hole of 1.5" (~0.06 pc). With an increase in sensitivity to accelerations by a factor of ~6 over our previous efforts, we are able to directly probe the kinematic structure of the young stellar disk, which appears to have an inner radius of 0.8". We find that candidate disk members are on eccentric orbits, with a mean eccentricity of = 0.30 +/- 0.07. Such eccentricities cannot be explained by the relaxation of a circular disk with a normal initial mass function, which suggests the existence of a top-heavy IMF or formation in an initially eccentric disk.Comment: 7 pages, 4 figures, SPIE Astronomical Telescopes and Instrumentation 201

Orbits and origins of the young stars in the central parsec of the galaxy

We present new proper motions from the 10 m Keck telescopes for a puzzling population of massive, young stars located within a parsec of the supermassive black hole at the Galactic Center. Our proper motion measurements have uncertainties of only 0.07 mas yr^(−1) (3 km s^(−1) ), which is ≳7 times better than previous proper motion measurements for these stars, and enables us to measure accelerations as low as 0.2 mas yr^(−2) (7 km s^(−1) yr^(−1) ). These measurements, along with stellar line-of-sight velocities from the literature, constrain the true orbit of each individual star and allow us to directly test the hypothesis that the massive stars reside in two stellar disks as has been previously proposed. Analysis of the stellar orbits reveals only one disk of young stars using a method that is capable of detecting disks containing at least 7 stars. The detected disk contains 50% (38 of 73) of the young stars, is inclined by ~115° from the plane of the sky, and is oriented at a position angle of ∼100° East of North. The on-disk and off-disk populations have similar K-band luminosity functions and radial distributions that decrease at larger radii as ∝ r^(−2). The disk has an out-of-the-disk velocity dispersion of 28±6 km s^(−1) , which corresponds to a half-opening angle of 7°±2° , and several candidate disk members have eccentricities greater than 0.2. Our findings suggest that the young stars may have formed in situ but in a more complex geometry than a simple thin circular disk

SiS in the circumstellar envelope of IRC +10126: maser and quasi-thermal emission

We present new Effelsberg-100 m, ATCA, and VLA observations of rotational SiS transitions in the circumstellar envelope (CSE) of IRC +10216. Thanks to the high angular resolution achieved by the ATCA observations, we unambiguously confirm that the molecule's J=1-0 transition exhibits maser action in this CSE, as first suggested more than thirty years ago. The maser emission's radial velocity peaking at a local standard of rest velocity of -39.862$\pm$0.065 km/s indicates that it arises from an almost fully accelerated shell. Monitoring observations show time variability of the SiS (1-0) maser. The two lowest-$J$ SiS quasi-thermal emission lines trace a much more extended emitting region than previous high-J SiS observations. Their distributions show that the SiS quasi-thermal emission consists of two components: one is very compact (radius<1.5", corresponding to <3$\times 10^{15}$ cm), and the other extends out to a radius >11". An incomplete shell-like structure is found in the north-east, which is indicative of existing SiS shells. Clumpy structures are also revealed in this CSE. The gain of the SiS (1-0) maser (optical depths of about -5 at the blue-shifted side and, assuming inversion throughout the entire line's velocity range, about -2 at the red-shifted side) suggests that it is unsaturated. The SiS (1-0) maser can be explained in terms of ro-vibrational excitation caused by infrared pumping, and we propose that infrared continuum emission is the main pumping source.Comment: Accepted for publication in ApJ. A high-resolution version can be found at https://gongyan2444.github.io/pdf/cw-leo-sis.pdf 3D movies of SiS cubes can be found at https://gongyan2444.github.io/movie/sis10-3d.avi and https://gongyan2444.github.io/movie/sis21-3d.av

Geometric structure of the generic static traversable wormhole throat

Traversable wormholes have traditionally been viewed as intrinsically topological entities in some multiply connected spacetime. Here, we show that topology is too limited a tool to accurately characterize a generic traversable wormhole: in general one needs geometric information to detect the presence of a wormhole, or more precisely to locate the wormhole throat. For an arbitrary static spacetime we shall define the wormhole throat in terms of a 2-dimensional constant-time hypersurface of minimal area. (Zero trace for the extrinsic curvature plus a "flare-out" condition.) This enables us to severely constrain the geometry of spacetime at the wormhole throat and to derive generalized theorems regarding violations of the energy conditions-theorems that do not involve geodesic averaging but nevertheless apply to situations much more general than the spherically symmetric Morris-Thorne traversable wormhole. [For example: the null energy condition (NEC), when suitably weighted and integrated over the wormhole throat, must be violated.] The major technical limitation of the current approach is that we work in a static spacetime-this is already a quite rich and complicated system.Comment: 25 pages; plain LaTeX; uses epsf.sty (four encapsulated postscript figures

Relaxation of strained silicon on Si0.5Ge0.5 virtual substrates

Strain relaxation has been studied in tensile strained silicon layers grown on Si0.5Ge0.5 virtual substrates, for layers many times the critical thickness, using high resolution x-ray diffraction. Layers up to 30 nm thick were found to relax less than 2% by the glide of preexisting 60° dislocations. Relaxation is limited because many of these dislocations dissociate into extended stacking faults that impede the dislocation glide. For thicker layers, nucleated microtwins were observed, which significantly increased relaxation to 14%. All these tensile strained layers are found to be much more stable than layers with comparable compressive strain

Testing for periodicities in near-IR light curves of Sgr A

We present the results of near-infrared (2 μm) monitoring of Sgr A*-IR with 1 minute time sampling using laser guide star adaptive optics (LGS AO) system at the Keck II telescope. Sgr A*-IR was observed continuously for up to three hours on each of seven nights, between 2006 May and 2007 August. Sgr A*-IR is detected at all times and is continuously variable. These observations allow us to investigate Nyquist sampled periods ranging from about 2 minutes to an hour. Of particular interest are periods of ~20 min, which corresponds to a quasi-periodic (QPO) signal claimed based upon previous near-infrared observations and interpreted as the orbit of a ’hot spot’ at or near the last stable orbit of a spinning black hole. We investigate these claims by comparing periodograms of the light curves with models for red noise and find no significant deviations that would indicate QPO activity at any time scale probed in the study. We find that the variability of Sgr A* is consistent with a model based on correlated noise with a power spectrum having a frequency dependence of ~ f^(2.5), consistent with that observed in AGNs. Furthermore, the periodograms show power down to the minimum sampling time of 2 min, well below the period of the last stable orbit of a maximally spinning black hole, indicating that the Sgr A*-IR light curves observed in this study is unlikely to be from the Keplerian motion of a single ’hot spot’ of orbiting plasma