Umbral Moonshine and the Niemeier Lattices

In this paper we relate umbral moonshine to the Niemeier lattices: the 23 even unimodular positive-definite lattices of rank 24 with non-trivial root systems. To each Niemeier lattice we attach a finite group by considering a naturally defined quotient of the lattice automorphism group, and for each conjugacy class of each of these groups we identify a vector-valued mock modular form whose components coincide with mock theta functions of Ramanujan in many cases. This leads to the umbral moonshine conjecture, stating that an infinite-dimensional module is assigned to each of the Niemeier lattices in such a way that the associated graded trace functions are mock modular forms of a distinguished nature. These constructions and conjectures extend those of our earlier paper, and in particular include the Mathieu moonshine observed by Eguchi-Ooguri-Tachikawa as a special case. Our analysis also highlights a correspondence between genus zero groups and Niemeier lattices. As a part of this relation we recognise the Coxeter numbers of Niemeier root systems with a type A component as exactly those levels for which the corresponding classical modular curve has genus zero.Comment: 181 pages including 95 pages of Appendices; journal version, minor typos corrected, Research in the Mathematical Sciences, 2014, vol.

Rare Decay Modes of Quarter BPS Dyons

The degeneracy of quarter BPS dyons in N=4 supersymmetric string theories is known to jump across walls of marginal stability on which a quarter BPS dyon can decay into a pair of half BPS dyons. We show that as long as the electric and magnetic charges of the original dyon are primitive elements of the charge lattice, the subspaces of the moduli space on which a quarter BPS dyon becomes marginally unstable against decay into a pair of quarter BPS dyons or a half BPS dyon and a quarter BPS dyon are of codimension two or more. As a result any pair of generic points in the moduli space can be connected by a path avoiding these subspaces and there is no jump in the spectrum associated with these subspaces.Comment: LaTeX file, 9 pages; v2: a minor logical error corrected with no change in the result

Global Transcriptomic Profiling of Bovine Endometrial Immune Response In Vitro. I. Effect of Lipopolysaccharide on Innate Immunity

The dysregulation of endometrial immune response to bacterial lipopolysaccharide (LPS) has been implicated in uterine disease and infertility in the postpartum dairy cow, although the mechanisms are not clear. Here, we investigated whole-transcriptomic gene expression in primary cultures of mixed bovine epithelial and stromal endometrial cells. Cultures were exposed to LPS for 6 h, and cellular response was measured by bovine microarray. Approximately 30% of the 1006 genes altered by LPS were classified as being involved in immune response. Cytokines and chemokines (IL1A, CX3CL1, CXCL2, and CCL5), interferon (IFN)-stimulated genes (RSAD2, MX2, OAS1, ISG15, and BST2), and the acute phase molecule SAA3 were the most up-regulated genes. Ingenuity Pathway Analysis identified up-regulation of many inflammatory cytokines and chemokines, which function to attract immune cells to the endometrium, together with vascular adhesion molecules and matrix metalloproteinases, which can facilitate immune cell migration from the tissue toward the uterine lumen. Increased expression of many IFN-signaling genes, immunoproteasomes, guanylate-binding proteins, and genes involved in the intracellular recognition of pathogens suggests important roles for these molecules in the innate defense against bacterial infections. Our findings confirmed the important role of endometrial cells in uterine innate immunity, whereas the global approach used identified several novel immune response pathways triggered by LPS in the endometrium. Additionally, many genes involved in endometrial response to the conceptus in early pregnancy were also altered by LPS, suggesting one mechanism whereby an ongoing response to infection may interfere with the establishment of pregnancy

Local density of states of a d-wave superconductor with inhomogeneous antiferromagnetic correlations

The tunneling spectrum of an inhomogeneously doped extended Hubbard model is calculated at the mean field level. Self-consistent solutions admit both superconducting and antiferromagnetic order, which coexist inhomogeneously because of spatial randomness in the doping. The calculations find that, as a function of doping, there is a continuous cross over from a disordered ``pinned smectic'' state to a relatively homogeneous d-wave state with pockets of antiferromagnetic order. The density of states has a robust d-wave gap, and increasing antiferromagnetic correlations lead to a suppression of the coherence peaks. The spectra of isolated nanoscale antiferromagnetic domains are studied in detail, and are found to be very different from those of macroscopic antiferromagnets. Although no single set of model parameters reproduces all details of the experimental spectrum in BSCCO, many features, notably the collapse of the coherence peaks and the occurence of a low-energy shoulder in the local spectrum, occur naturally in these calculations.Comment: 9 pages, 5 figure

k-String tensions and the 1/N expansion

We address the question of whether the large-N expansion in pure SU(N) gauge theories requires that k-string tensions must have a power series expansion in 1/N^2, as in the sine law, or whether 1/N contributions are also allowable, as in Casimir scaling. We find that k-string tensions may, in fact, have 1/N corrections, and consistency with the large-N expansion in the open-string sector depends crucially on an exact cancellation, which we will prove, among terms involving odd powers of 1/N in particular combinations of Wilson loops. It is shown how these cancellations are fulfilled, and consistency with the large-N expansion achieved, in a concrete example, namely, strong-coupling lattice gauge theory with the heat-kernel action. This is a model which has both a 1/N^2 expansion and Casimir scaling of the k-string tensions. Analysis of the closed string channel in this model confirms our conclusions, and provides further insights into the large-N dependence of energy eigenstates and eigenvalues.Comment: RevTeX4, 21 pages. Typos corrected, references added, some discussions expanded; conclusions unchanged. Version to appear on PR

Controllable Andreev retroreflection and specular Andreev reflection in a four-terminal graphene-superconductor hybrid system

We report the investigation of electron transport through a four-terminal graphene-superconductor hybrid system. Due to the quantum interference of the reflected holes from two graphene-superconductor interfaces with phase difference $\theta$, it is found that the specular Andreev reflection vanishes at $\theta=0$ while the Andreev retroreflection disappears at $\theta=\pi$. This means that the retroreflection and specular reflection can be easily controlled and separated in this device. In addition, due to the diffraction effect in the narrow graphene nanoribbon, the reflected hole can exit from both graphene terminals. As the width of nanoribbon increases, the diffraction effect gradually disappears and the reflected hole eventually exits from a particular graphene terminal depending on the type of Andreev reflection.Comment: 4 pages, 5 figure