Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop

We study three-point functions of operators on the $1/2$ BPS Wilson loop in planar $\mathcal{N}=4$ super Yang-Mills theory. The operators we consider are "defect changing operators", which change the scalar coupled to the Wilson loop. We first perform the computation at two loops in general set-ups, and then study a special scaling limit called the ladders limit, in which the spectrum is known to be described by a quantum mechanics with the SL(2,$\mathbb{R}$) symmetry. In this limit, we resum the Feynman diagrams using the Schwinger-Dyson equation and determine the structure constants at all order in the rescaled coupling constant. Besides providing an interesting solvable example of defect conformal field theories, our result gives invaluable data for the integrability-based approach to the structure constants.Comment: 31 pages + appendices; v2 References adde

Cosmic Microwave Background-Weak Lensing Correlation: Analytical and Numerical Study of Nonlinearity and Implications for Dark Energy

Evolution of density fluctuations yields secondary anisotropies in the cosmic microwave background ( CMB), which are correlated with the same density fluctuations that can be measured by weak lensing (WL) surveys. We study the CMB-WL correlation induced by the integrated Sachs-Wolfe (ISW) effect and its nonlinear extension, the Rees-Sciama (RS) effect, using analytical models as well as N-body simulations. We show that an analytical model based on the time derivative of matter power spectrum agrees with simulations. All-sky cosmic-variance-limited CMB and WL surveys allow us to measure the correlation from the nonlinear RS effect with high significance (50 sigma) for l(max) = 10(4) whereas forthcoming missions such as Planck and LSST are expected to yield 4 l p 10 1.5 sigma detections, on the assumption of that the point-source contributions are negligible. We find that the CMB-WL correlation has a characteristic scale which is sensitive to the nature of dark energy.Alfred P. Sloan FellowshipAstronom

Matter Distribution around Galaxies

We explore the mass distribution of material associated with galaxies from the observation of gravitational weak lensing for the galaxy mass correlation function with the aid of $N$-body simulations of dark matter. The latter is employed to unfold various contributions that contribute to the integrated line of sight mass density. We conclude that galaxies have no definite edges of the matter distribution, extending to the middle to neighbouring galaxies with the density profile roughly $r^{-2.4}$ beyond the virial radius. The mass distributed beyond the virial radius (gravitationally bound radius) explains the gap seen in the mass density estimates, the global value $\Omega_m\sim 0.27$ and typically $\Omega_{\rm gal} \sim 0.15$ from the luminosity density multiplied by the mass to light ratio. We suggest to use a physical method of gravitational lensing to characterise galaxy samples rather than characterise them with photometric means.Comment: 16 pages, 5 figures. ApJ accepte

Thorough elucidation of synthesis and structure of poly(glycerol) functionalized nanodiamonds

Poly(glycerol) (PG) is one of the most promising platforms for the surface modification of nanomaterials especially for in vivo applications. Since the “grafting-from” process is facile to functionalize the nanomaterial surface covalently through the ring-opening polymerization of glycidol (GD), it has been applied to a variety of nanomaterials. The resulting numerous hydroxy groups in the hyperbranched structure serve as scaffolds for further functionalization and provide good dispersibility under physiological conditions. On the other hand, nanodiamond (ND) is a nanomaterial most intensely worked with PG because of its prominent properties including fluorescence from color centers. Despite the wide-spread use, the process has not been extended to be scalable and controllable. In addition, the structural details of PG chain on ND surface are yet elusive. In this work, we develop more scalable and safer PG functionalization of NDs by dropwise-addition of GD to ethylene glycol (EG) suspension of ND. The resulting PG amount can be controlled or even estimated by the reaction conditions (weights of GD, ND and EG) and the ND properties (diameter and oxygen content). The structure of PG chain was qualitatively and quantitatively analyzed by ¹³C nuclear magnetic resonance (NMR) and dynamic light scattering (DLS) measurements. Based on these results, the structure of PG is elucidated

New NTP analogs: the synthesis of 4′-thioUTP and 4′-thioCTP and their utility for SELEX

The synthesis of the triphosphates of 4′-thiouridine and 4′-thiocytidine, 4′-thioUTP (7; thioUTP) and 4′-thioCTP (8; thioCTP), and their utility for SELEX (systematic evolution of ligands by exponential enrichment) is described. The new nucleoside triphosphate (NTP) analogs 7 and 8 were prepared from appropriately protected 4′-thiouridine and -cytidine derivatives using the one-pot method reported by J. Ludwig and F. Eckstein [(1989) J. Org. Chem., 54, 631–635]. Because SELEX requires both in vitro transcription and reverse transcription, we examined the ability of 7 and 8 for SELEX by focusing on the two steps. Incorporation of 7 and 8 by T7 RNA polymerase to give 4′-thioRNA (thioRNA) proceeded well and was superior to those of the two sets of frequently used modified NTP analogs for SELEX (2′-NH(2)dUTP and 2′-NH(2)dCTP; 2′-FdUTP and 2′-FdCTP), when an adequate leader sequence of DNA template was selected. We revealed that a leader sequence of about +15 of DNA template is important for the effective incorporation of modified NTP analogs by T7 RNA polymerase. In addition, reverse transcription of the resulting thioRNA into the complementary DNA in the presence of 2′-deoxynucleoside triphosphates (dNTPs) also proceeded smoothly and precisely. The stability of the thioRNA toward RNase A was 50 times greater than that of the corresponding natural RNA. With these successful results in hand, we attempted the selection of thioRNA aptamers to human α-thrombin using thioUTP and thioCTP, and found a thioRNA aptamer with high binding affinity (K(d) = 4.7 nM)

Simulations of Early Baryonic Structure Formation with Stream Velocity: I. Halo Abundance

It has been recently shown that the relative velocity between the dark matter and the baryons (vbc) at the time of recombination can affect the structure formation in the early universe (Tseliakhovich & Hirata 2010). We statistically quantify this effect using large cosmological simulations. We use three different high resolution sets of simulations (with separate transfer functions for baryons and dark matter) that vary in box size, particle number, and the value of the relative velocity between dark matter and baryons. We show that the total number density of halos is suppressed by ~ 20% at z = 25 for vbc = 1{\sigma}(vbc), where {\sigma}(vbc) is the variance of the relative velocity, while for vbc = 3.4{\sigma}(vbc) the relative suppression at the same redshift reaches 50%, remaining at or above the 30% level all the way to z = 11. We also find high abundance of "empty halos", i.e., halos that have gas fraction below half of the cosmic mean baryonic fraction fb. Specifically we find that for vbc = 1{\sigma}(vbc) all halos below 10^5M\odot are empty at z \geq 19. The high abundance of empty halos results in significant delay in the formation of gas rich mini-halos and the first galaxies.Comment: 7 pages, 8 figures, accepted to Ap