Cartan-Weyl 3-algebras and the BLG Theory I: Classification of Cartan-Weyl 3-algebras

As Lie algebras of compact connected Lie groups, semisimple Lie algebras have wide applications in the description of continuous symmetries of physical systems. Mathematically, semisimple Lie algebra admits a Cartan-Weyl basis of generators which consists of a Cartan subalgebra of mutually commuting generators H_I and a number of step generators E^\alpha that are characterized by a root space of non-degenerate one-forms \alpha. This simple decomposition in terms of the root space allows for a complete classification of semisimple Lie algebras. In this paper, we introduce the analogous concept of a Cartan-Weyl Lie 3-algebra. We analyze their structure and obtain a complete classification of them. Many known examples of metric Lie 3-algebras (e.g. the Lorentzian 3-algebras) are special cases of the Cartan-Weyl 3-algebras. Due to their elegant and simple structure, we speculate that Cartan-Weyl 3-algebras may be useful for describing some kinds of generalized symmetries. As an application, we consider their use in the Bagger-Lambert-Gustavsson (BLG) theory.Comment: LaTeX. 34 pages.v2. deleted some distracting paragraphs in the introduction to bring more out the main results of the paper. typos corrected and references adde

On thermodynamics of N=6 superconformal Chern-Simons theory

We study thermodynamics of N=6 superconformal Chern-Simons theory by computing quantum corrections to the free energy. We find that in weakly coupled ABJM theory on R(2) x S(1), the leading correction is non-analytic in the 't Hooft coupling lambda, and is approximately of order lambda^2 log(lambda)^3. The free energy is expressed in terms of the scalar thermal mass m, which is generated by screening effects. We show that this mass vanishes to 1-loop order. We then go on to 2-loop order where we find a finite and positive mass squared m^2. We discuss differences in the calculation between Coulomb and Lorentz gauge. Our results indicate that the free energy is a monotonic function in lambda which interpolates smoothly to the N^(3/2) behaviour at strong coupling.Comment: 29 pages. v2: references added. v3: minor changes, references added, published versio

Association between maternal depression symptoms across the first eleven years of their child’s life and subsequent offspring suicidal ideation

Depression is common, especially in women of child-bearing age; prevalence estimates for this group range from 8% to 12%, and there is robust evidence that maternal depression is associated with mental health problems in offspring. Suicidal behaviour is a growing concern amongst young people and those exposed to maternal depression are likely to be especially at high risk. The aim of this study was to utilise a large, prospective population cohort to examine the relationship between depression symptom trajectories in mothers over the first eleven years of their child’s life and subsequent adolescent suicidal ideation. An additional aim was to test if associations were explained by maternal suicide attempt and offspring depressive disorder. Data were utilised from a population-based birth cohort: the Avon Longitudinal Study of Parents and Children. Maternal depression symptoms were assessed repeatedly from pregnancy to child age 11 years. Offspring suicidal ideation was assessed at age 16 years. Using multiple imputation, data for 10,559 families were analysed. Using latent class growth analysis, five distinct classes of maternal depression symptoms were identified (minimal, mild, increasing, sub-threshold, chronic-severe). The prevalence of past-year suicidal ideation at age 16 years was 15% (95% CI: 14-17%). Compared to offspring of mothers with minimal symptoms, the greatest risk of suicidal ideation was found for offspring of mothers with chronic-severe symptoms [OR 3.04 (95% CI 2.19,4.21)], with evidence for smaller increases in risk of suicidal ideation in offspring of mothers with sub-threshold, increasing and mild symptoms. These associations were not fully accounted for by maternal suicide attempt or offspring depression diagnosis. Twenty-six percent of non-depressed offspring of mothers with chronic-severe depression symptoms reported suicidal ideation. Risk for suicidal ideation should be considered in young people whose mothers have a history of sustained high levels of depression symptoms, even when the offspring themselves do not have a depression diagnosis

Measurement of vector boson scattering and constraints on anomalous quartic couplings from events with four leptons and two jets in proton-proton collisions at root s=13 TeV

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Search for dijet resonances in proton-proton collisions at root s=13 TeV and constraints on dark matter and other models

Correction: DOI:10.1016/j.physletb.2017.09.029Peer reviewe

Search for new physics with dijet angular distributions in proton-proton collisions at root S = 13 TeV

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Search for light bosons in decays of the 125 GeV Higgs boson in proton-proton collisions at root s=8 TeV

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