The Operator Product Expansion of the Lowest Higher Spin Current at Finite N

For the N=2 Kazama-Suzuki(KS) model on CP^3, the lowest higher spin current with spins (2, 5/2, 5/2,3) is obtained from the generalized GKO coset construction. By computing the operator product expansion of this current and itself, the next higher spin current with spins (3, 7/2, 7/2, 4) is also derived. This is a realization of the N=2 W_{N+1} algebra with N=3 in the supersymmetric WZW model. By incorporating the self-coupling constant of lowest higher spin current which is known for the general (N,k), we present the complete nonlinear operator product expansion of the lowest higher spin current with spins (2, 5/2, 5/2, 3) in the N=2 KS model on CP^N space. This should coincide with the asymptotic symmetry of the higher spin AdS_3 supergravity at the quantum level. The large (N,k) 't Hooft limit and the corresponding classical nonlinear algebra are also discussed.Comment: 62 pages; the footnotes added, some redundant appendices removed, the presentations in the whole paper improved and to appear in JHE

The Primary Spin-4 Casimir Operators in the Holographic SO(N) Coset Minimal Models

Starting from SO(N) current algebra, we construct two lowest primary higher spin-4 Casimir operators which are quartic in spin-1 fields. For N is odd, one of them corresponds to the current in the WB_{\frac{N-1}{2}} minimal model. For N is even, the other corresponds to the current in the WD_{\frac{N}{2}} minimal model. These primary higher spin currents, the generators of wedge subalgebra, are obtained from the operator product expansion of fermionic (or bosonic) primary spin-N/2 field with itself in each minimal model respectively. We obtain, indirectly, the three-point functions with two real scalars, in the large N 't Hooft limit, for all values of the 't Hooft coupling which should be dual to the three-point functions in the higher spin AdS_3 gravity with matter.Comment: 65 pages; present the main results only and to appear in JHEP where one can see the Appendi

More on N=1 Matrix Model Curve for Arbitrary N

Using both the matrix model prescription and the strong-coupling approach, we describe the intersections of n=0 and n=1 non-degenerated branches for quartic (polynomial of adjoint matter) tree-level superpotential in N=1 supersymmetric SO(N)/USp(2N) gauge theories with massless flavors. We also apply the method to the degenerated branch. The general matrix model curve on the two cases we obtain is valid for arbitrary N and extends the previous work from strong-coupling approach. For SO(N) gauge theory with equal massive flavors, we also obtain the matrix model curve on the degenerated branch for arbitrary N. Finally we discuss on the intersections of n=0 and n=1 non-degenerated branches for equal massive flavors.Comment: 36pp; to appear in JHE

The one-round Voronoi game replayed

We consider the one-round Voronoi game, where player one (``White'', called ``Wilma'') places a set of n points in a rectangular area of aspect ratio r <=1, followed by the second player (``Black'', called ``Barney''), who places the same number of points. Each player wins the fraction of the board closest to one of his points, and the goal is to win more than half of the total area. This problem has been studied by Cheong et al., who showed that for large enough $n$ and r=1, Barney has a strategy that guarantees a fraction of 1/2+a, for some small fixed a. We resolve a number of open problems raised by that paper. In particular, we give a precise characterization of the outcome of the game for optimal play: We show that Barney has a winning strategy for n>2 and r>sqrt{2}/n, and for n=2 and r>sqrt{3}/2. Wilma wins in all remaining cases, i.e., for n>=3 and r<=sqrt{2}/n, for n=2 and r<=sqrt{3}/2, and for n=1. We also discuss complexity aspects of the game on more general boards, by proving that for a polygon with holes, it is NP-hard to maximize the area Barney can win against a given set of points by Wilma.Comment: 14 pages, 6 figures, Latex; revised for journal version, to appear in Computational Geometry: Theory and Applications. Extended abstract version appeared in Workshop on Algorithms and Data Structures, Springer Lecture Notes in Computer Science, vol.2748, 2003, pp. 150-16

Lyman alpha line formation in starbursting galaxies II. Extremely Thick, Dustless, and Static HI Media

The Lya line transfer in an extremely thick medium of neutral hydrogen is investigated by adopting an accelerating scheme in our Monte Carlo code to skip a large number of core or resonant scatterings. This scheme reduces computing time significantly with no sacrifice in the accuracy of the results. We applied this numerical method to the Lya transfer in a static, uniform, dustless, and plane-parallel medium. Two types of photon sources have been considered, the midplane source and the uniformly distributed sources. The emergent profiles show double peaks and absorption trough at the line-center. We compared our results with the analytic solutions derived by previous researchers, and confirmed that both solutions are in good agreement with each other. We investigated the directionality of the emergent Lya photons and found that limb brightening is observed in slightly thick media while limb darkening appears in extremely thick media. The behavior of the directionality is noted to follow that of the Thomson scattered radiation in electron clouds, because both Lya wing scattering and Thomson scattering share the same Rayleigh scattering phase function. The mean number of wing scatterings just before escape is in exact agreement with the prediction of the diffusion approximation. The Lya photons constituting the inner part of the emergent profiles follow the relationship derived from the diffusion approximation. We present a brief discussion on the application of our results to the formation of Lya broad absorption troughs and P-Cygni type Lya profiles seen in the UV spectra of starburst galaxies.Comment: 24 papges, 12 figures, The revised version submitted to Ap

Reference solar irradiance spectra and consequences of their disparities in remote sensing of the ocean colour

International audienceSatellite ocean colour missions require a standard extraterrestrial solar irradiance spectrum in the visible and near-infrared (NIR) for use in the process of radiometric calibration, atmospheric correction and normalization of water-leaving radiances from in-situ measurements. There are numerous solar irradiance spectra (or models) currently in use within the ocean colour community and related domains. However, these irradiance spectra, constructed from single and/or multiple measurements sets or models, have noticeable differences ? ranging from about ±1% in the NIR to ±6% in the short wavelength region (ultraviolet and blue) ? caused primarily by the variation in the solar activity and uncertainties in experimental data from different instruments. Such differences between the applied solar irradiance spectra may have quite important consequences in reconciliation, comparison and validation of the products resulting from different ocean colour instruments. Thus, it is prudent to examine the model-to-model differences and ascertain an appropriate solar irradiance spectrum for use in future ocean colour research and validation purposes. This study first describes the processes which generally require the application of a solar irradiance spectrum, and then investigates the eight solar irradiance spectra (widely in use within the remote sensing community) selected on the basis of the following criteria: minimum spectral range of 350?1200 nm with adequate spectral resolution, completely or mostly based on direct measurements, minimal error range, intercomparison with other experiments and update of data. The differences in these spectra in absolute terms and in the SeaWiFS and MERIS in-band irradiances and their consequences on the retrieval algorithms of chlorophyll and suspended sediment are analyzed. Based on these detailed analyses, this study puts forward the solar irradiance spectrum most appropriate for all aspects of research, calibration and validation in ocean colour remote sensing. For an improved approximation of the extraterrestrial solar spectrum in the ultraviolet-NIR domain this study also proposes a new solar constant value determined from space-borne measurements of the last three decades

Singly-Peaked P-Cygni type Lyα\alpha from starburst galaxies

We present results of Monte Carlo calculations for the Lya line transfer in an expanding dusty supershell, where Lya source is a well-localized star cluster in a starburst galaxy.The escape of Lya photons from such system is achieved by a number of back-scattering, and so a series of emission peaks are formed redward of the systemic redshift by back-scattering. However, majority of observed Lya emission from starbursts show singly-peaked asymmetric profiles. We find in this paper that, in order to form a singly-peaked Lya emission, dust should be distributed in the ionized bubble, as well as within the supershell of neutral hydrogen. We also find that the overall escape fraction of Lya photons is determined by the HI column density of the supershell, the expansion velocity of the supershell, and the spatial distribution of dust. However, the kinematic information of the expanding supershell is preserved in the profile of Lya emission even when the supershell is dusty. Our results are potentially useful to fit the P-Cygni type Lya line profiles from starburst galaxies, either nearby galaxies or high-z Lyman break galaxies (LBGs).Comment: Original version was submitted to MNRAS on 13, Jan, 2003, which was withdrawn. After heavey revison, its essence was resubmitted to ApJL on 18 Aug. 2003. 2nd revision. 10 pages, 3 figure

The Large N 't Hooft Limit of Kazama-Suzuki Model

We consider N=2 Kazama-Suzuki model on CP^N=SU(N+1)/SU(N)xU(1). It is known that the N=2 current algebra for the supersymmetric WZW model, at level k, is a nonlinear algebra. The N=2 W_3 algebra corresponding to N=2 was recovered from the generalized GKO coset construction previously. For N=4, we construct one of the higher spin currents, in N=2 W_5 algebra, with spins (2, 5/2, 5/2, 3). The self-coupling constant in the operator product expansion of this current and itself depends on N as well as k explicitly. We also observe a new higher spin primary current of spins (3, 7/2, 7/2, 4). From the behaviors of N=2, 4 cases, we expect the operator product expansion of the lowest higher spin current and itself in N=2 W_{N+1} algebra. By taking the large (N, k) limit on the various operator product expansions in components, we reproduce, at the linear order, the corresponding operator product expansions in N=2 classical W_{\infty}^{cl}[\lambda] algebra which is the asymptotic symmetry of the higher spin AdS_3 supergravity found recently.Comment: 44 pages; the two typos in the first paragraph of page 23 corrected and to appear in JHE