15626289
Half-BPS SU(N) correlators in = 4 SYM
In this note we study half-BPS operators in = 4 super Yang-Mills for gauge group SU(N) at finite N. In particular we elaborate on the results of hep-th/0410236, providing an exact formula for the null basis operators algorithmically constructed there. For gauge groups U(N) and SU(N) we show that this basis is dual to the basis of multi-trace operators with respect to the two point function. We use this to extend the results of hep-th/0611290 concerning factorisation and probabilities from U(N) to SU(N). We also give a construction for a separate diagonal basis of the SU(N) operators in terms of the higher Hamiltonians of the complex matrix model reduction of this sector.
14643488
Diagonal multi-matrix correlators and BPS operators in N=4 SYM
We present a complete basis of multi-trace multi-matrix operators that has a diagonal two point function for the free matrix field theory at finite N. This generalises to multiple matrices the single matrix diagonalisation by Schur polynomials. Crucially, it involves intertwining the gauge group U(N) and the global symmetry group U(M) with Clebsch-Gordan coefficients of symmetric groups Sn. When applied to = 4 super Yang-Mills we consider the U(3) subgroup of the full symmetry group. The diagonalisation allows the description of a dual basis to multi-traces, which permits the characterisation of the metric on operators transforming in short representations at weak coupling. This gives a framework for the comparison of quarter and eighth-BPS giant gravitons of AdS5 × S5 spacetime to gauge invariant operators of the dual = 4 SYM.
118163488
Gauge/gravity duality beyond the planar limit
One of the most exciting and successful ideas pursued in string theory is gauge/gravity duality. We consider the example of the AdS/CFT correspondence, which maps maximally supersymmetric Yang-Mills (N = 4 SYM) in four dimensions with gauge group U(N) to closed strings propagating in a background of Anti de Sitter space crossed with a sphere (AdS5 × S5). Much progress has been made understanding this duality in the planar ’t Hooft limit, where we fix the coupling of the gauge theory λ and take N large. On the gravity side the string coupling gs is proportional to 1/N for fixed λ, so in this limit we get classical string theory. In this thesis we use symmetric group methods to study the AdS/CFT correspondence exactly at finite N , without taking the planar limit. This takes the string theory into the quantum regime and allows us to probe phenomena which are non-perturbative in gs. First we enumerate the spectrum. While the spectrum is non-trivial in the planar limit, it is further complicated at finite N by the Stringy Exclusion Principle, which truncates the usual trace spectrum. We organise local operators in the gauge theory using representations of the gauge group U(N), which for heavy operators are interpreted in terms of giant graviton branes in the bulk. To do this we sort the different fields of the theory into representations of the global superconformal symmetry group using SchurWeyl duality. We then compute twoand three-point functions of these operators exactly to all orders in N for the free theory and at one loop. We use these correlation functions to resolve certain transition probabilities for giant gravitons using CFT factorisation.
118845537
Correlators, probabilities and topologies in = 4 SYM
We calculate transition probabilities for various processes involving giant gravitons and small gravitons in AdS space, using the dual = 4 SYM theory. The normalization factors for these probabilities involve, in general, correlators for manifolds of non-trivial topology which are obtained by gluing simpler four-manifolds. This follows from the factorization properties which relate CFT correlators for different topologies. These points are illustrated, in the first instance, in the simpler example of a two dimensional Matrix CFT. We give the bulk five dimensional interpretation, involving neighborhoods of Witten graphs, of these gluing properties of the four dimensional boundary CFT. As a corollary we give a simple description, based on Witten graphs, of a multiplicity of bulk topologies corresponding to a fixed boundary topology. We also propose to interpret the correlators as topology-changing transition amplitudes between LLM geometries.
7045461
Permutations and the loop
We consider the one-loop two-point function for multi-trace operators in the U(2) sector of = 4 supersymmetric Yang-Mills at finite N. We derive an expression for it in terms of U(N) and Sn+1 group theory data, where n is the length of the operators. The Clebsch-Gordan operators constructed in [1], which are diagonal at tree level, only mix at one loop if you can reach the same (n+1)-box Young diagram by adding a single box to each of the n-box Young diagrams of their U(N) representations (which organise their multi-trace structure). Similar results are expected for higher loops and for other sectors of the global symmetry group.
119293956
The Kepler Asteroseismic Investigation: Scientific goals and first results
Kepler is a NASA mission designed to detect exoplanets and characterize the properties of exoplanetary systems. Kepler also includes an asteroseismic programme which is being conducted through the Kepler Asteroseismic Science Consortium (KASC), whose 400 members are organized into 13 working groups by type of variable star. So far data have been available from the first 7 month of the mission containing a total of 2937 targets observed at a 1-min cadence for periods between 10 days and 7 months. The goals of the asteroseismic part of the Kepler project is to perform detailed studies of stellar interiors. The first results of the asteroseismic analysis are orders of magnitude better than seen before, and this bodes well for how the future analysis of Kepler data for many types of stars will impact our general understanding of stellar structure and evolution (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
119267981
Kepler Mission Design, Realized Photometric Performance, and Early Science
The Kepler Mission, launched on 2009 March 6, was designed with the explicit capability to detect Earth-size planets in the habitable zone of solar-like stars using the transit photometry method. Results from just 43 days of data along with ground-based follow-up observations have identified five new transiting planets with measurements of their masses, radii, and orbital periods. Many aspects of stellar astrophysics also benefit from the unique, precise, extended, and nearly continuous data set for a large number and variety of stars. Early results for classical variables and eclipsing stars show great promise. To fully understand the methodology, processes, and eventually the results from the mission, we present the underlying rationale that ultimately led to the flight and ground system designs used to achieve the exquisite photometric performance. As an example of the initial photometric results, we present variability measurements that can be used to distinguish dwarf stars from red giants.
22980504
The Solar Acoustic Spectrum and Eigenmode Parameters
The Global Oscillation Network Group (GONG) project estimates the frequencies, amplitudes, and linewidths of more than 250,000 acoustic resonances of the sun from data sets lasting 36 days. The frequency resolution of a single data set is 0.321 microhertz. For frequencies averaged over the azimuthal order m, the median formal error is 0.044 microhertz, and the associated median fractional error is 1.6 × 10−5. For a 3-year data set, the fractional error is expected to be 3 × 10−6. The GONG m-averaged frequency measurements differ from other helioseismic data sets by 0.03 to 0.08 microhertz. The differences arise from a combination of systematic errors, random errors, and possible changes in solar structure.
16588713
Exoplanets or Dynamic Atmospheres? The Radial Velocity and Line Shape Variations of 51 Pegasi and τ Bootis
The stars 51 Pegasi and τ Bootis show radial velocity variations that have been interpreted as resulting from companions with roughly Jovian mass and orbital periods of a few days. Gray and Gray & Hatzes reported that the radial velocity signal of 51 Peg is synchronous with variations in the shape of the line λ6253 Fe I; thus, they argue that the velocity signal arises not from a companion of planetary mass but from dynamic processes in the atmosphere of the star, possibly nonradial pulsations. Here we seek confirming evidence for line shape or strength variations in both 51 Peg and τ Boo, using R = 50,000 observations taken with the Advanced Fiber Optic Echelle. Because of our relatively low spectral resolution, we compare our observations with Gray's line bisector data by fitting observed line profiles to an expansion in terms of orthogonal (Hermite) functions. To obtain an accurate comparison, we model the emergent line profiles from rotating and pulsating stars, taking the instrumental point-spread function into account. We describe this modeling process in detail. We find no evidence for line profile or strength variations at the radial velocity period in either 51 Peg or in τ Boo. For 51 Peg, our upper limit for line shape variations with 4.23 day periodicity is small enough to exclude with 10 σ confidence the bisector curvature signal reported by Gray & Hatzes; the bisector span and relative line depth signals reported by Gray are also not seen, but in this case with marginal (2 σ) confidence. We cannot, however, exclude pulsations as the source of 51 Peg's radial velocity variation because our models imply that line shape variations associated with pulsations should be much smaller than those computed by Gray & Hatzes; these smaller signals are below the detection limits both for Gray & Hatzes's data and for our own. τ Boo's large radial velocity amplitude and v sin i make it easier to test for pulsations in this star. Again we find no evidence for periodic line shape changes, at a level that rules out pulsations as the source of the radial velocity variability. We conclude that the planet hypothesis remains the most likely explanation for the existing data.
4403395
Transiting extrasolar planetary candidates in the Galactic bulge
More than 200 extrasolar planets have been discovered around relatively nearby stars, primarily through the Doppler line shifts owing to reflex motions of their host stars, and more recently through transits of some planets across the faces of the host stars. The detection of planets with the shortest known periods, 1.2–2.5 days, has mainly resulted from transit surveys which have generally targeted stars more massive than 0.75 M[circdot], where M[circdot] is the mass of the Sun. Here we report the results from a planetary transit search performed in a rich stellar field towards the Galactic bulge. We discovered 16 candidates with orbital periods between 0.4 and 4.2 days, five of which orbit stars of masses in the range 0.44–0.75 M[circdot]. In two cases, radial-velocity measurements support the planetary nature of the companions. Five candidates have orbital periods below 1.0 day, constituting a new class of ultra-short-period planets, which occur only around stars of less than 0.88 M[circdot]. This indicates that those orbiting very close to more-luminous stars might be evaporatively destroyed or that jovian planets around stars of lower mass might migrate to smaller radii.