Coulomb Branch Operators and Mirror Symmetry in Three Dimensions

We develop new techniques for computing exact correlation functions of a class of local operators, including certain monopole operators, in three-dimensional $\mathcal{N} = 4$ abelian gauge theories that have superconformal infrared limits. These operators are position-dependent linear combinations of Coulomb branch operators. They form a one-dimensional topological sector that encodes a deformation quantization of the Coulomb branch chiral ring, and their correlation functions completely fix the ($n\leq 3$)-point functions of all half-BPS Coulomb branch operators. Using these results, we provide new derivations of the conformal dimension of half-BPS monopole operators as well as new and detailed tests of mirror symmetry. Our main approach involves supersymmetric localization on a hemisphere $HS^3$ with half-BPS boundary conditions, where operator insertions within the hemisphere are represented by certain shift operators acting on the $HS^3$ wavefunction. By gluing a pair of such wavefunctions, we obtain correlators on $S^3$ with an arbitrary number of operator insertions. Finally, we show that our results can be recovered by dimensionally reducing the Schur index of 4D $\mathcal{N} = 2$ theories decorated by BPS 't Hooft-Wilson loops.Comment: 92 pages plus appendices, two figures; v2 and v3: typos corrected, references adde

Constitutional Law—New York State’s Textbook Loan Law Not a Law Respecting an Establishment of Religion in Violation of the First and Fourteenth Amendments of the United States Constitution

Board of Education of Central District No. 1 v. Allen, 392 U.S. 236 (1968)

SOME ULTRASTRUCTURAL EFFECTS OF INSULIN, HYDROCORTISONE, AND PROLACTIN ON MAMMARY GLAND EXPLANTS

The effects of insulin, hydrocortisone, and prolactin on the morphology of explants from midpregnant mouse mammary glands were studied. Insulin promotes the formation of daughter cells within the alveolar epithelium which are ultrastructurally indistinguishable from the parent cells. The addition of hydrocortisone to the medium containing insulin brings the daughter cells to a new, intermediate level of ultrastructural development by effecting an extensive increase of the rough endoplasmic reticulum (RER) throughout the cytoplasm and an increase in the lateral paranuclear Golgi apparatus. When prolactin is added to the insulin-hydrocortisone medium, the daughter cells complete their ultrastructural differentiation. There is a translocation of the RER, Golgi apparatus, and nucleus and the appearance of secretory protein granules within the cytoplasm. There is excellent correlation between the ultrastructural appearance of the alveoli and their capacity to synthesize casein

Hamiltonian solutions of the 3-body problem in (2+1)-gravity

We present a full study of the 3-body problem in gravity in flat (2+1)-dimensional space-time, and in the nonrelativistic limit of small velocities. We provide an explicit form of the ADM Hamiltonian in a regular coordinate system and we set up all the ingredients for canonical quantization. We emphasize the role of a U(2) symmetry under which the Hamiltonian is invariant and which should generalize to a U(N-1) symmetry for N bodies. This symmetry seems to stem from a braid group structure in the operations of looping of particles around each other, and guarantees the single-valuedness of the Hamiltonian. Its role for the construction of single-valued energy eigenfunctions is also discussed.Comment: 25 pages, no figure. v2: some calculation details removed to make the paper more concise (see v1 for the longer version), minor correction in a formula in the section on quantization, references added; results and conclusions unchange

Anticipatory Smiling: Linking Early Affective Communication and Social Outcome

In anticipatory smiles, infants appear to communicate pre-existing positive affect by smiling at an object and then turning the smile toward an adult. We report two studies in which the precursors, development, and consequences of anticipatory smiling were investigated. Study 1 revealed a positive correlation between infant smiling at 6 months and the level of anticipatory smiling at 8 and 10 months during joint attention episodes, as well as a positive correlation between anticipatory smiling and parent-rated social expressivity scores at 30 months. Study 2 confirmed a developmental increase in the number of infants using anticipatory smiles between 9 and 12 months that had been initially documented in the Study 1 sample [Venezia, M., Messinger, D. S., Thorp, D., & Mundy, P. (2004). The development of anticipatory smiling. Infancy, 6(3), 397–406]. Additionally, anticipatory smiling at 9 months positively predicted parent-rated social competence scores at 30 months. Findings are discussed with regard to the importance of anticipatory smiling in early socioemotional development

Neutrophil survival on biomaterials is determined by surface topography

AbstractPurpose: Cardiovascular device-centered infections are a major cause of hospital morbidity, mortality, and expense. Caused by opportunistic bacteria, this phenomenon is thought to arise because of a defect in neutrophil bacterial killing. We have shown that neutrophils that adhere to polystyrene remain viable, whereas neutrophils that adhere to the vascular biomaterials expanded polytetrafluoroethylene (ePTFE) and Dacron undergo a rapid nonapoptotic death. This study was designed to test the hypothesis that surface topography is a determinant of the nonapoptotic death response of neutrophils to biomaterials. Methods: We took advantage of the ease with which a polystyrene surface can be manipulated to examine the effect of surface topography on neutrophil viability. Neutrophils were exposed to smooth or roughened polystyrene surfaces both in vivo and in vitro. Changes in cell membrane permeability and production of reactive oxygen species by individual cells were monitored with fluorescent dyes. Results: Host cells and isolated human neutrophils died rapidly after adhesion to roughened polystyrene. Neutrophils adherent to roughened surfaces produced more reactive oxygen intermediates than those adherent to smooth surfaces and were first to die. The cell death response precipitated by expanded polytetrafluoroethylene, Dacron, or the roughened surfaces was significantly reduced with treatment of the neutrophils with catalase, diphenylene iodonium, or the src kinase inhibitor PP2 before adhesion. Conclusions: Neutrophil adhesion to roughened materials triggers rapid production of reactive oxygen species and precipitates a nonapoptotic cell death. Understanding the material properties that trigger these responses is essential to development of the next generation of implantable biomaterials. (J Vasc Surg 2003;37:1082-90.

Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions

The Lanczos-Lovelock models of gravity constitute the most general theories of gravity in D dimensions which satisfy (a) the principle of of equivalence, (b) the principle of general co-variance, and (c) have field equations involving derivatives of the metric tensor only up to second order. The mth order Lanczos-Lovelock Lagrangian is a polynomial of degree m in the curvature tensor. The field equations resulting from it become trivial in the critical dimension $D = 2m$ and the action itself can be written as the integral of an exterior derivative of an expression involving the vierbeins, in the differential form language. While these results are well known, there is some controversy in the literature as to whether the Lanczos-Lovelock Lagrangian itself can be expressed as a total divergence of quantities built only from the metric and its derivatives (without using the vierbeins) in $D = 2m$. We settle this issue by showing that this is indeed possible and provide an algorithm for its construction. In particular, we demonstrate that, in two dimensions, $R \sqrt{-g} = \partial_j R^j$ for a doublet of functions $R^j = (R^0,R^1)$ which depends only on the metric and its first derivatives. We explicitly construct families of such R^j -s in two dimensions. We also address related questions regarding the Gauss-Bonnet Lagrangian in $D = 4$. Finally, we demonstrate the relation between the Chern-Simons form and the mth order Lanczos-Lovelock Lagrangian.Comment: 15 pages, no figure