A note on perturbation series in supersymmetric gauge theories

Exact results in supersymmetric Chern-Simons and N=2 Yang-Mills theories can be used to examine the quantum behavior of observables and the structure of the perturbative series. For the U(2) x U(2) ABJM model, we determine the asymptotic behavior of the perturbative series for the partition function and write it as a Borel transform. Similar results are obtained for N=2 SU(2) super Yang-Mills theory with four fundamental flavors and in N=2* super Yang-Mills theory, for the partition function as well as for the expectation values for Wilson loop and 't Hooft loop operators (in the 0 and 1 instanton sectors). In all examples, one has an alternate perturbation series where the coefficient of the nth term increases as n!, and the perturbation series are Borel summable. We also calculate the expectation value for a Wilson loop operator in the N=2* SU(N) theory at large N in different regimes of the 't Hooft gauge coupling and mass parameter. For large masses, the calculation reproduces the running gauge coupling for the pure N=2 SYM theory.Comment: 28 pages. V2: minor additions and reference adde

Height estimates for Killing graphs

The paper aims at proving global height estimates for Killing graphs defined over a complete manifold with nonempty boundary. To this end, we first point out how the geometric analysis on a Killing graph is naturally related to a weighted manifold structure, where the weight is defined in terms of the length of the Killing vector field. According to this viewpoint, we introduce some potential theory on weighted manifolds with boundary and we prove a weighted volume estimate for intrinsic balls on the Killing graph. Finally, using these tools, we provide the desired estimate for the weighted height in the assumption that the Killing graph has constant weighted mean curvature and the weighted geometry of the ambient space is suitably controlled.Comment: 26 pages. Final version. To appear on Journal of Geometric Analysi

An instability of higher-dimensional rotating black holes

We present the first example of a linearized gravitational instability of an asymptotically flat vacuum black hole. We study perturbations of a Myers-Perry black hole with equal angular momenta in an odd number of dimensions. We find no evidence of any instability in five or seven dimensions, but in nine dimensions, for sufficiently rapid rotation, we find perturbations that grow exponentially in time. The onset of instability is associated with the appearance of time-independent perturbations which generically break all but one of the rotational symmetries. This is interpreted as evidence for the existence of a new 70-parameter family of black hole solutions with only a single rotational symmetry. We also present results for the Gregory-Laflamme instability of rotating black strings, demonstrating that rotation makes black strings more unstable.Comment: 38 pages, 13 figure

Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match

We compute three-point functions of single trace operators in planar N=4 SYM. We consider the limit where one of the operators is much smaller than the other two. We find a precise match between weak and strong coupling in the Frolov-Tseytlin classical limit for a very general class of classical solutions. To achieve this match we clarify the issue of back-reaction and identify precisely which three-point functions are captured by a classical computation.Comment: 36 pages. v2: figure added, references adde

Undrained expansion of a cylindrical cavity in clays with fabric anisotropy: theoretical solution

This paper presents a novel, exact, semi-analytical solution for the quasi-static undrained expansion of a cylindrical cavity in soft soils with fabric anisotropy. This is the first theoretical solution of the undrained expansion of a cylindrical cavity under plane strain conditions for soft soils with anisotropic behaviour of plastic nature. The solution is rigorously developed in detail, introducing a new stress invariant to deal with the soil fabric. The semianalytical solution requires numerical evaluation of a system of six first-order ordinary differential equations. The results agree with finite element analyses and show the influence of anisotropic plastic behaviour. The effective stresses at critical state are constant, and they may be analytically related to the undrained shear strength. The initial vertical cross-anisotropy caused by soil deposition changes towards a radial cross-anisotropy after cavity expansion. The analysis of the stress paths shows that proper modelling of anisotropic plastic behaviour involves modelling not only the initial fabric anisotropy but also its evolution with plastic straining.The research was initiated as part of GEO-INSTALL (Modelling Installation Effects in Geotechnical Engineering, PIAP-GA-2009-230638) and CREEP (Creep of Geomaterials, PIAP-GA-2011-286397) projects supported by the European Community through the programme Marie Curie Industry-Academia Partnerships and Pathways (IAPP) under the 7th Framework Programme

A single, one-off measure of depression and anxiety predicts future symptoms, higher healthcare costs, and lower quality of life in coronary heart disease patients: Analysis from a multi-wave, primary care cohort study

To determine whether a one-off, baseline measure of depression and anxiety in a primary care, coronary heart disease (CHD) population predicts ongoing symptoms, costs, and quality of life across a 3-year follow-up.Longitudinal cohort study.16 General Practice surgeries across South-East London.803 adults (70% male, mean age 71 years) contributing up to 7 follow-up points.Ongoing reporting of symptoms, health care costs, and quality of life.At baseline, 27% of the sample screened positive for symptoms of depression and anxiety, as measured by the Hospital Anxiety and Depression Scale (HADS). The probability of scoring above the cut-off throughout the follow-up was 71.5% (p<0.001) for those screening positive at baseline, and for those screening negative, the probability of scoring below the cut-off throughout the follow-up was 97.6% (p<0.001). Total health care costs were 39% higher during follow-up for those screening positive (p<0.05). Quality of life as measured by the SF-12 was lower on the mental component during follow-up for those screening positive (-0.75, CI -1.53 to 0.03, p = 0.059), and significantly lower on the physical component (-4.99, CI -6.23 to -.376, p<0.001).A one-off measure for depression and anxiety symptoms in CHD predicts future symptoms, costs, and quality of life over the subsequent three-years. These findings suggest symptoms of depression and anxiety in CHD persist throughout long periods and are detrimental to a patient's quality of life, whilst incurring higher health care costs for primary and secondary care services. Screening for these symptoms at the primary care level is important to identify and manage patients at risk of the negative effects of this comorbidity. Implementation of screening, and possible collaborative care strategies and interventions that help mitigate this risk should be the ongoing focus of researchers and policy-makers