1793441
Diagonal free field matrix correlators, global symmetries and giant gravitons
We obtain a basis of diagonal free field multi-matrix 2-point correlators in a theory with global symmetry group G. The operators fall into irreducible representations of G. This applies for gauge group U(N) at finite N. For composites made of n fundamental fields, this is expressed in terms of Clebsch-Gordan coefficients for the decomposition of the n-fold tensor products of the fundamental field representation in terms of G × Sn representations. We use this general construction in the case of the SL(2) sector of = 4 SYM. In this case, by using oscillator constructions, we reduce the computation of the relevant Clebsch-Gordans coupling infinite dimensional discrete series irreps of SL(2) to a problem in symmetric groups. Applying these constructions we write down gauge invariant operators with a Fock space structure similar to that arising in a large angular momentum limit of worldvolume excitations of giant gravitons. The Fock space structure emerges from Clebsch multiplicities of tensor products of symmetric group representations. We also give the action of the 1-loop dilatation operator of = 4 SYM on this basis of multi-matrix operators.
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.
51811786
Complex matrix model duality
The same complex matrix model calculates both tachyon scattering for the c=1 noncritical string at the self-dual radius and certain correlation functions of operators which preserve half the supersymmetry in N=4 super-Yang-Mills theory. It is dual to another complex matrix model where the couplings of the first model are encoded in the Kontsevich-like variables of the second. The duality between the theories is mirrored by the duality of their Feynman diagrams. Analogously to the Hermitian Kontsevich-Penner model, the correlation functions of the second model can be written as sums over discrete points in subspaces of the moduli space of punctured Riemann surfaces.
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.
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.
118717986
Asteroseismic Investigation of Known Planet Hosts in the Kepler Field
In addition to its great potential for characterizing extra-solar planetary systems, the Kepler Mission is providing unique data on stellar oscillations. A key aspect of Kepler asteroseismology is the application to solar-like oscillations of main-sequence stars. As an example, we here consider an initial analysis of data for three stars in the Kepler field for which planetary transits were known from ground-based observations. For one of these, HAT-P-7, we obtain a detailed frequency spectrum and hence strong constraints on the stellar properties. The remaining two stars show definite evidence for solar-like oscillations, yielding a preliminary estimate of their mean densities.
14396627
Deep Optical Photometry of Six Fields in the Andromeda Galaxy
Using the Advanced Camera for Surveys on the Hubble Space Telescope, we have obtained deep optical images reaching well below the oldest main-sequence turnoff in six fields of the Andromeda Galaxy. The fields fall at four positions on the southeast minor axis, one position in the giant stellar stream, and one position on the northeast major axis. These data were obtained as part of three large observing programs designed to probe the star formation history of the stellar population in various structures of the galaxy. In this paper, we present the images, catalogs, and artificial star tests for these observing programs as a supplement to the analyses published previously. These high-level science products are also archived at the Multimission Archive at the Space Telescope Science Institute.
317593
Evidence for Flash Mixing in He-rich sdB Stars
We present FUSE spectra of three He-rich sdB stars. Two of these stars, PG1544+488 and JL87, reveal extremely strong C III lines, suggesting that they have mixed triple-α carbon from the deep interior out to their surfaces. Using TLUSTY NLTE line-blanketed model atmospheres, we find that PG1544+488 has a surface composition of 96% He, 2% C, and 1% N. JL87 shows a similar surface enrichment of C and N but still retains a significant amount of hydrogen. In contrast, the third star, LB1766, is devoid of hydrogen and strongly depleted of carbon, indicating that its surface material has undergone CN-cycle processing.We interpret these observations with new evolutionary calculations which suggest that He-rich sdB stars with C-rich compositions arise from a delayed helium-core flash on the white-dwarf cooling curve. During such a flash the interior convection zone will penetrate into the stellar envelope, thereby mixing the envelope with the He- and C-rich core. Such “flash-mixed” stars will arrive on the extreme horizontal branch (EHB) with He- and C-rich surface compositions and will be hotter than the hottest canonical EHB stars. Two types of flash mixing are possible:“deep” and “shallow”, depending on whether the hydrogen envelope is mixed deeply into the site of the helium flash or only with the outer layers of the core. Based on both their stellar parameters and surface compositions, we suggest that PG1544+488 and JL87 are examples of “deep” and “shallow” flash mixing, respectively.
18259911
Evidence for a Significant Intermediate-Age Population in the M31 Halo from Main Sequence Photometry
We present a color-magnitude diagram (CMD) for a minor-axis field in the halo of the Andromeda galaxy (M31), 51' (11 kpc) from the nucleus. These observations, taken with the Advanced Camera for Surveys (ACS) on the Hubble Space Telescope, are the deepest optical images yet obtained, attaining 50% completeness at mV = 30.7 mag. The CMD, constructed from ~3 × 105 stars, reaches more than 1.5 mag fainter than the old main-sequence turnoff. Our analysis is based on direct comparisons to ACS observations of four globular clusters through the same filters, as well as χ2 fitting to a finely spaced grid of calibrated stellar-population models. We find that the M31 halo contains a major (~30% by mass) intermediate-age (6-8 Gyr) metal-rich ([Fe/H] > -0.5) population, as well as a significant globular cluster age (11-13.5 Gyr) metal-poor population. These findings support the idea that galaxy mergers played an important role in the formation of the M31 halo.
17765307
Halos of Spiral Galaxies. I. The Tip of the Red Giant Branch as a Distance Indicator
We have imaged the halo populations of a sample of nearby spiral galaxies using the Wide Field Planetary Camera 2 on board the Hubble Space Telescope with the aim of studying the stellar population properties and relating them to those of the host galaxies. In four galaxies, the red giant branch is sufficiently well populated to measure the magnitude of the tip of the red giant branch (TRGB), a well-known distance indicator. Using both the Sobel edge-detection technique and maximum likelihood analysis to measure the I-band magnitude of the TRGB, we determine distances to four nearby galaxies: NGC 253, NGC 4244, NGC 4945, and NGC 4258. For the first three galaxies, the TRGB distance is here determined more directly, and is likely to be more accurate, than previous distance estimates. In the case of NGC 4258, our TRGB distance is in good agreement with the geometrical maser distance, supporting the Large Magellanic Cloud distance modulus (m - M)0 = 18.50 that is generally adopted in recent estimates of the Hubble constant.