Quantum D-modules for toric nef complete intersections

On a smooth projective variety with k ample line bundles, we denote by Z the complete intersection subvariety defined by generic sections. We define the twisted quantum D-module which is a vector bundle with a flat connection, a flat pairing and a natural integrable structure. An appropriate quotient of it is isomorphic to the ambient part of the quantum D-module of Z. When the variety is toric, these quantum D-modules are cyclic. The twisted quantum D-module can be presented via mirror symmetry by the GKZ system associated to the total space of the dual of the direct sum of these line bundles. A question is to know what is the system of equations that define the ambiant part of the quantum D-module of Z. We construct this system as a quotient ideal of the GKZ system. We also state and prove the non-equivariant twisted Gromov-Witten axioms in the appendix.Comment: 39 pages, accepted to International Journal of Mathematic

Quantum Serre theorem as a duality between quantum D-modules

We give an interpretation of quantum Serre of Coates and Givental as a duality of twisted quantum D-modules. This interpretation admits a non-equivariant limit, and we obtain a precise relationship among (1) the quantum D-module of X twisted by a convex vector bundle E and the Euler class, (2) the quantum D-module of the total space of the dual bundle E^\vee over X, and (3) the quantum D-module of a submanifold Z\subset X cut out by a regular section of E. When E is the anticanonical line bundle K_X^{-1}, we identify these twisted quantum D-modules with second structure connections with different parameters, which arise as Fourier-Laplace transforms of the quantum D-module of X. In this case, we show that the duality pairing is identified with Dubrovin's second metric (intersection form).Comment: 40 pages, v2: the title has changed, exposition improved and references added, accepted for publication in International Mathematics Research Notice

From conic intersections to toric intersections: The case of the isoptic curves of an ellipse

Starting from the study of the orthoptic curves of parabolas and ellipses, we generalize to the case of isoptic curves for any angle, i.e. the geometric locus of points from which a parabola or an ellipse are viewed under a given angle. This leads to the investigation of spiric curves and to the construction of these curves as an actual intersection of a self-intersecting torus with a plane. The usage of a Computer Algebra System facilitated this investigation

A New Test of the Einstein Equivalence Principle and the Isotropy of Space

Recent research has established that nonsymmetric gravitation theories like Moffat's NGT predict that a gravitational field singles out an orthogonal pair of polarization states of light that propagate with different phase velocities. We show that a much wider class of nonmetric theories encompassed by the $\chi g$ formalism predict such violations of the Einstein equivalence principle. This gravity-induced birefringence of space implies that propagation through a gravitational field can alter the polarization of light. We use data from polarization measurements of extragalactic sources to constrain birefringence induced by the field of the Galaxy. Our new constraint is $10^8$ times sharper than previous ones.Comment: 21 pages, Latex, 3 Postscript figure

A rocky planet transiting a nearby low-mass star

M-dwarf stars -- hydrogen-burning stars that are smaller than 60 per cent of the size of the Sun -- are the most common class of star in our Galaxy and outnumber Sun-like stars by a ratio of 12:1. Recent results have shown that M dwarfs host Earth-sized planets in great numbers: the average number of M-dwarf planets that are between 0.5 to 1.5 times the size of Earth is at least 1.4 per star. The nearest such planets known to transit their star are 39 parsecs away, too distant for detailed follow-up observations to measure the planetary masses or to study their atmospheres. Here we report observations of GJ 1132b, a planet with a size of 1.2 Earth radii that is transiting a small star 12 parsecs away. Our Doppler mass measurement of GJ 1132b yields a density consistent with an Earth-like bulk composition, similar to the compositions of the six known exoplanets with masses less than six times that of the Earth and precisely measured densities. Receiving 19 times more stellar radiation than the Earth, the planet is too hot to be habitable but is cool enough to support a substantial atmosphere, one that has probably been considerably depleted of hydrogen. Because the host star is nearby and only 21 per cent the radius of the Sun, existing and upcoming telescopes will be able to observe the composition and dynamics of the planetary atmosphere.Comment: Published in Nature on 12 November 2015, available at http://dx.doi.org/10.1038/nature15762. This is the authors' version of the manuscrip

A Scientific Name for Pacific Oysters

WOS:000447083800041International audienc

Wavelet-Based Linear-Response Time-Dependent Density-Functional Theory

Linear-response time-dependent (TD) density-functional theory (DFT) has been implemented in the pseudopotential wavelet-based electronic structure program BigDFT and results are compared against those obtained with the all-electron Gaussian-type orbital program deMon2k for the calculation of electronic absorption spectra of N2 using the TD local density approximation (LDA). The two programs give comparable excitation energies and absorption spectra once suitably extensive basis sets are used. Convergence of LDA density orbitals and orbital energies to the basis-set limit is significantly faster for BigDFT than for deMon2k. However the number of virtual orbitals used in TD-DFT calculations is a parameter in BigDFT, while all virtual orbitals are included in TD-DFT calculations in deMon2k. As a reality check, we report the x-ray crystal structure and the measured and calculated absorption spectrum (excitation energies and oscillator strengths) of the small organic molecule N-cyclohexyl-2-(4-methoxyphenyl)imidazo[1,2-a]pyridin-3-amine

Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function

We evaluate the one loop determinant of matter multiplet fields of N=4 supergravity in the near horizon geometry of quarter BPS black holes, and use it to calculate logarithmic corrections to the entropy of these black holes using the quantum entropy function formalism. We show that even though individual fields give non-vanishing logarithmic contribution to the entropy, the net contribution from all the fields in the matter multiplet vanishes. Thus logarithmic corrections to the entropy of quarter BPS black holes, if present, must be independent of the number of matter multiplet fields in the theory. This is consistent with the microscopic results. During our analysis we also determine the complete spectrum of small fluctuations of matter multiplet fields in the near horizon geometry.Comment: LaTeX file, 52 pages; v2: minor corrections, references adde

Duality Invariant Actions and Generalised Geometry

We construct the non-linear realisation of the semi-direct product of E(11) and its first fundamental representation at lowest order and appropriate to spacetime dimensions four to seven. This leads to a non-linear realisation of the duality groups and introduces fields that depend on a generalised space which possess a generalised vielbein. We focus on the part of the generalised space on which the duality groups alone act and construct an invariant action.Comment: 59 pages (typos fixed and added comments

Chemical Genetic Analysis and Functional Characterization of Staphylococcal Wall Teichoic Acid 2-Epimerases Reveals Unconventional Antibiotic Drug Targets

Here we describe a chemical biology strategy performed in Staphylococcus aureus and Staphylococcus epidermidis to identify MnaA, a 2-epimerase that we demonstrate interconverts UDP-GlcNAc and UDP-ManNAc to modulate substrate levels of TarO and TarA wall teichoic acid (WTA) biosynthesis enzymes. Genetic inactivation of mnaA results in complete loss of WTA and dramatic in vitro β-lactam hypersensitivity in methicillin-resistant S. aureus (MRSA) and S. epidermidis (MRSE). Likewise, the β-lactam antibiotic imipenem exhibits restored bactericidal activity against mnaA mutants in vitro and concomitant efficacy against 2-epimerase defective strains in a mouse thigh model of MRSA and MRSE infection. Interestingly, whereas MnaA serves as the sole 2-epimerase required for WTA biosynthesis in S. epidermidis, MnaA and Cap5P provide compensatory WTA functional roles in S. aureus. We also demonstrate that MnaA and other enzymes of WTA biosynthesis are required for biofilm formation in MRSA and MRSE. We further determine the 1.9Å crystal structure of S. aureus MnaA and identify critical residues for enzymatic dimerization, stability, and substrate binding. Finally, the natural product antibiotic tunicamycin is shown to physically bind MnaA and Cap5P and inhibit 2-epimerase activity, demonstrating that it inhibits a previously unanticipated step in WTA biosynthesis. In summary, MnaA serves as a new Staphylococcal antibiotic target with cognate inhibitors predicted to possess dual therapeutic benefit: as combination agents to restore β-lactam efficacy against MRSA and MRSE and as non-bioactive prophylactic agents to prevent Staphylococcal biofilm formation.publishe