A Metric for Gradient RG Flow of the Worldsheet Sigma Model Beyond First Order

Tseytlin has recently proposed that an action functional exists whose gradient generates to all orders in perturbation theory the Renormalization Group (RG) flow of the target space metric in the worldsheet sigma model. The gradient is defined with respect to a metric on the space of coupling constants which is explicitly known only to leading order in perturbation theory, but at that order is positive semi-definite, as follows from Perelman's work on the Ricci flow. This gives rise to a monotonicity formula for the flow which is expected to fail only if the beta function perturbation series fails to converge, which can happen if curvatures or their derivatives grow large. We test the validity of the monotonicity formula at next-to-leading order in perturbation theory by explicitly computing the second-order terms in the metric on the space of coupling constants. At this order, this metric is found not to be positive semi-definite. In situations where this might spoil monotonicity, derivatives of curvature become large enough for higher order perturbative corrections to be significant.Comment: 15 pages; Erroneous sentence in footnote 14 removed; this version therefore supersedes the published version (our thanks to Dezhong Chen for the correction

Complete Calabi-Yau metrics from Kahler metrics in D=4

In the present work the local form of certain Calabi-Yau metrics possessing a local Hamiltonian Killing vector is described in terms of a single non linear equation. The main assumptions are that the complex $(3,0)$-form is of the form $e^{ik}\widetilde{\Psi}$, where $\widetilde{\Psi}$ is preserved by the Killing vector, and that the space of the orbits of the Killing vector is, for fixed value of the momentum map coordinate, a complex 4-manifold, in such a way that the complex structure of the 4-manifold is part of the complex structure of the complex 3-fold. The link with the solution generating techniques of [26]-[28] is made explicit and in particular an example with holonomy exactly SU(3) is found by use of the linearization of [26], which was found in the context of D6 branes wrapping a holomorphic 1-fold in a hyperkahler manifold. But the main improvement of the present method, unlike the ones presented in [26]-[28], does not rely in an initial hyperkahler structure. Additionally the complications when dealing with non linear operators over the curved hyperkahler space are avoided by use of this method.Comment: Version accepted for publication in Phys.Rev.

Epizootie dans un peuplement de gardons

Guilhon Jean, Besse P. Épizootie dans un peuplement de Gardons. In: Bulletin de l'Académie Vétérinaire de France tome 102 n°9, 1949. pp. 373-376

Potential one-forms for hyperk\"ahler structures with torsion

It is shown that an HKT-space with closed parallel potential 1-form has $D(2,1;-1)$-symmetry. Every locally conformally hyperk\"ahler manifold generates this type of geometry. The HKT-spaces with closed parallel potential 1-form arising in this way are characterized by their symmetries and an inhomogeneous cubic condition on their torsion.Comment: 16 pages, Latex, no figure

Taille de la population d’Avahi laniger dans la réserve d’Ambodiriana-Manompana, Nord-est de Madagascar

Avahi laniger est le seul lémurien nocturne appartenant à la famille des Indriidae qui habite les forêts humides de l’est de Madagascar (Mittermeier et. al., 2010) dont une partie disparaît chaque année (exploitation du bois, pratique du «tavy» ou culture sur brûlis) (Beaucent and Fayolle, 2011; Lehman and Wright, 2000). La fragmentation et la destruction de leur habitat ainsi que la chasse menacent la survie de nombreuses espèces de lémuriens incluant celle de A. laniger (Jenkins et. al., 2011; Rakotondravony and Rabenandrasana, 2011; Anderson, Rowcliffe and Cowlishaw, 2007). Nous avons réalisé, entre fin Avril et Mai 2012, une étude de densité de la population de A. laniger au sein de l’aire protégée de Manompana-Ambodiriana afin d’estimer la taille de la population totale et de déterminer l’impact du projet de conservation menée par l’Association de Défense de la Forêt d’Ambodiriana (ADEFA) qui recherche l’évolution démographique à moyen terme de cette espèce."LABEX" TULIP: (ANR-10-LABX-41), fct fellowship: (SFRH/BD/64875/2009)

The Joint Crisis Plan: A Powerful Tool to Promote Mental Health.

Purpose: The Joint Crisis Plan (JCP) has received growing interest in clinical and research settings. JCP is a type of psychiatric advance statement that describes how to recognize early signs of crisis and how to manage crises. The purpose of the present study, to our knowledge the first to be conducted on this topic in the French-speaking context and to include inpatients, was to describe the content of JCPs and how they are perceived by patients and the providers. Methods: The study used an exploratory, mixed, sequential method. Existing JCPs were retrospectively collected in several clinical contexts (hospital, community settings, and sheltered accommodation). Based on their analyses, we conducted semi-structured interviews including some rating scales on the perception of the JCPs among patients and providers in these settings. For the qualitative analyses, content analyses were conducted with a hybrid approach using NVivo 12 software. Data were double-coded and discussed with a third researcher until agreement was reached. Results: One hundred eighty-four JCPs were collected retrospectively and 24 semi-structured interviews were conducted with 12 patients and 12 providers. No relatives could be included in the research process. The content of the studied JCPs was relevant and indicated that patients had good knowledge of themselves and their illness. Improvements in the quality of the therapeutic relationship, respect for patients' choices and wishes, and a greater sense of control of their illness were reported. The JCP was perceived as a very useful tool by patients and providers. Concerning JCP limitations, lack of staff training, difficulties with the shared decision-making process, and the poor availability of the JCPs when needed were reported. Conclusion: The study highlights that JCPs may be used with patients suffering from a large variety of psychiatric disorders in different care settings. The JCP is perceived as very useful by both patients and providers. The promising results of this study support the promotion of the wide use of JCPs with patients who have experienced crises. It is important to continue to research JCPs through impact studies that include family members

Asymptotically Hyperbolic Non Constant Mean Curvature Solutions of the Einstein Constraint Equations

We describe how the iterative technique used by Isenberg and Moncrief to verify the existence of large sets of non constant mean curvature solutions of the Einstein constraints on closed manifolds can be adapted to verify the existence of large sets of asymptotically hyperbolic non constant mean curvature solutions of the Einstein constraints.Comment: 19 pages, TeX, no figure

A Reilly formula and eigenvalue estimates for differential forms

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a Riemannian manifold. The equality case of our inequality gives rise to a number of rigidity results, when the geometry of the boundary has special properties and the domain is non-negatively curved. Finally we also obtain, as a by-product of our calculations, an upper bound of the first eigenvalue of the Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.Comment: 22 page

Remarks on evolution of space-times in 3+1 and 4+1 dimensions

A large class of vacuum space-times is constructed in dimension 4+1 from hyperboloidal initial data sets which are not small perturbations of empty space data. These space-times are future geodesically complete, smooth up to their future null infinity, and extend as vacuum space-times through their Cauchy horizon. Dimensional reduction gives non-vacuum space-times with the same properties in 3+1 dimensions.Comment: 10pp, exposition improved; final versio