The geometry of recursion operators

We study the fields of endomorphisms intertwining pairs of symplectic structures. Using these endomorphisms we prove an analogue of Moser's theorem for simultaneous isotopies of two families of symplectic forms. We also consider the geometric structures defined by pairs and triples of symplectic forms for which the squares of the intertwining endomorphisms are plus or minus the identity. For pairs of forms we recover the notions of symplectic pairs and of holomorphic symplectic structures. For triples we recover the notion of a hypersymplectic structure, and we also find three new structures that have not been considered before. One of these is the symplectic formulation of hyper-Kaehler geometry, which turns out to be a strict generalization of the usual definition in terms of differential or Kaehler geometry.Comment: cosmetic changes only; to appear in Comm. Math. Phy

Holomorphic Factorization for a Quantum Tetrahedron

We provide a holomorphic description of the Hilbert space H(j_1,..,j_n) of SU(2)-invariant tensors (intertwiners) and establish a holomorphically factorized formula for the decomposition of identity in H(j_1,..,j_n). Interestingly, the integration kernel that appears in the decomposition formula turns out to be the n-point function of bulk/boundary dualities of string theory. Our results provide a new interpretation for this quantity as being, in the limit of large conformal dimensions, the exponential of the Kahler potential of the symplectic manifold whose quantization gives H(j_1,..,j_n). For the case n=4, the symplectic manifold in question has the interpretation of the space of "shapes" of a geometric tetrahedron with fixed face areas, and our results provide a description for the quantum tetrahedron in terms of holomorphic coherent states. We describe how the holomorphic intertwiners are related to the usual real ones by computing their overlap. The semi-classical analysis of these overlap coefficients in the case of large spins allows us to obtain an explicit relation between the real and holomorphic description of the space of shapes of the tetrahedron. Our results are of direct relevance for the subjects of loop quantum gravity and spin foams, but also add an interesting new twist to the story of the bulk/boundary correspondence.Comment: 45 pages; published versio

Fermions in three-dimensional spinfoam quantum gravity

We study the coupling of massive fermions to the quantum mechanical dynamics of spacetime emerging from the spinfoam approach in three dimensions. We first recall the classical theory before constructing a spinfoam model of quantum gravity coupled to spinors. The technique used is based on a finite expansion in inverse fermion masses leading to the computation of the vacuum to vacuum transition amplitude of the theory. The path integral is derived as a sum over closed fermionic loops wrapping around the spinfoam. The effects of quantum torsion are realised as a modification of the intertwining operators assigned to the edges of the two-complex, in accordance with loop quantum gravity. The creation of non-trivial curvature is modelled by a modification of the pure gravity vertex amplitudes. The appendix contains a review of the geometrical and algebraic structures underlying the classical coupling of fermions to three dimensional gravity.Comment: 40 pages, 3 figures, version accepted for publication in GER

Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV

A search for a Higgs boson decaying into two photons is described. The analysis is performed using a dataset recorded by the CMS experiment at the LHC from pp collisions at a centre-of-mass energy of 7 TeV, which corresponds to an integrated luminosity of 4.8 inverse femtobarns. Limits are set on the cross section of the standard model Higgs boson decaying to two photons. The expected exclusion limit at 95% confidence level is between 1.4 and 2.4 times the standard model cross section in the mass range between 110 and 150 GeV. The analysis of the data excludes, at 95% confidence level, the standard model Higgs boson decaying into two photons in the mass range 128 to 132 GeV. The largest excess of events above the expected standard model background is observed for a Higgs boson mass hypothesis of 124 GeV with a local significance of 3.1 sigma. The global significance of observing an excess with a local significance greater than 3.1 sigma anywhere in the search range 110-150 GeV is estimated to be 1.8 sigma. More data are required to ascertain the origin of this excess.Comment: Submitted to Physics Letters

Measurement of isolated photon production in pp and PbPb collisions at sqrt(sNN) = 2.76 TeV

Isolated photon production is measured in proton-proton and lead-lead collisions at nucleon-nucleon centre-of-mass energies of 2.76 TeV in the pseudorapidity range |eta|<1.44 and transverse energies ET between 20 and 80 GeV with the CMS detector at the LHC. The measured ET spectra are found to be in good agreement with next-to-leading-order perturbative QCD predictions. The ratio of PbPb to pp isolated photon ET-differential yields, scaled by the number of incoherent nucleon-nucleon collisions, is consistent with unity for all PbPb reaction centralities.Comment: Submitted to Physics Letters

Testing microscopically derived descriptions of nuclear collectivity : Coulomb excitation of 22Mg

Many-body nuclear theory utilizing microscopic or chiral potentials has developed to the point that collectivity might be studied within a microscopic or ab initio framework without the use of effective charges; for example with the proper evolution of the E2 operator, or alternatively, through the use of an appropriate and manageable subset of particle–hole excitations. We present a precise determination of E2 strength in 22Mg and its mirror 22Ne by Coulomb excitation, allowing for rigorous comparisons with theory. No-core symplectic shell-model calculations were performed and agree with the new B(E2) values while in-medium similarity-renormalization-group calculations consistently underpredict the absolute strength, with the missing strength found to have both isoscalar and isovector components. The discrepancy between two microscopic models demonstrates the sensitivity of E2 strength to the choice of many-body approximation employed

Loss-of-Function Mutations in the Cell-Cycle Control Gene CDKN2A Impact on Glucose Homeostasis in Humans.

At the CDKN2A/B locus, three independent signals for type 2 diabetes risk are located in a non-coding region near CDKN2A. The disease-associated alleles have been implicated in reduced β-cell function, but the underlying mechanism remains elusive. In mice, β-cell specific loss of Cdkn2a causes hyperplasia whilst overexpression leads to diabetes, highlighting CDKN2A as a candidate effector transcript. Rare CDKN2A loss-of-function mutations are a cause of familial melanoma and offer the opportunity to determine the impact of CDKN2A haploinsufficiency on glucose homeostasis in humans. To test the hypothesis that such individuals have improved β-cell function, we performed oral and intravenous glucose tolerance tests on mutation carriers and matched controls. Compared with controls, carriers displayed increased insulin secretion, impaired insulin sensitivity and reduced hepatic insulin clearance. These results are consistent with a model whereby CDKN2A-loss affects a range of different tissues, including pancreatic β-cells and liver. To test for direct effects of CDKN2A-loss on β-cell function, we performed knockdown in a human β-cell line, EndoC-bH1. This revealed increased insulin secretion independent of proliferation. Overall, we demonstrate that CDKN2A is an important regulator of glucose homeostasis in humans, thus supporting its candidacy as an effector transcript for type 2 diabetes-associated alleles in the region

Loss-of-Function Mutations in the Cell-Cycle Control Gene CDKN2A Impact on Glucose Homeostasis in Humans.

At the CDKN2A/B locus, three independent signals for type 2 diabetes risk are located in a non-coding region near CDKN2A. The disease-associated alleles have been implicated in reduced β-cell function, but the underlying mechanism remains elusive. In mice, β-cell specific loss of Cdkn2a causes hyperplasia whilst overexpression leads to diabetes, highlighting CDKN2A as a candidate effector transcript. Rare CDKN2A loss-of-function mutations are a cause of familial melanoma and offer the opportunity to determine the impact of CDKN2A haploinsufficiency on glucose homeostasis in humans. To test the hypothesis that such individuals have improved β-cell function, we performed oral and intravenous glucose tolerance tests on mutation carriers and matched controls. Compared with controls, carriers displayed increased insulin secretion, impaired insulin sensitivity and reduced hepatic insulin clearance. These results are consistent with a model whereby CDKN2A-loss affects a range of different tissues, including pancreatic β-cells and liver. To test for direct effects of CDKN2A-loss on β-cell function, we performed knockdown in a human β-cell line, EndoC-bH1. This revealed increased insulin secretion independent of proliferation. Overall, we demonstrate that CDKN2A is an important regulator of glucose homeostasis in humans, thus supporting its candidacy as an effector transcript for type 2 diabetes-associated alleles in the region