7,242 research outputs found
Infrared Consistency and the Weak Gravity Conjecture
The weak gravity conjecture (WGC) asserts that an Abelian gauge theory
coupled to gravity is inconsistent unless it contains a particle of charge
and mass such that . This criterion is obeyed by all
known ultraviolet completions and is needed to evade pathologies from stable
black hole remnants. In this paper, we explore the WGC from the perspective of
low-energy effective field theory. Below the charged particle threshold, the
effective action describes a photon and graviton interacting via
higher-dimension operators. We derive infrared consistency conditions on the
parameters of the effective action using i) analyticity of light-by-light
scattering, ii) unitarity of the dynamics of an arbitrary ultraviolet
completion, and iii) absence of superluminality and causality violation in
certain non-trivial backgrounds. For convenience, we begin our analysis in
three spacetime dimensions, where gravity is non-dynamical but has a physical
effect on photon-photon interactions. We then consider four dimensions, where
propagating gravity substantially complicates all of our arguments, but bounds
can still be derived. Operators in the effective action arise from two types of
diagrams: those that involve electromagnetic interactions (parameterized by a
charge-to-mass ratio ) and those that do not (parameterized by a
coefficient ). Infrared consistency implies that is bounded from
below for small .Comment: 37 pages, 5 figures. Minor typos fixed and equation numbers changed
to match journal. Published in JHE
Hidden Simplicity of the Gravity Action
We derive new representations of the Einstein-Hilbert action in which
graviton perturbation theory is immensely simplified. To accomplish this, we
recast the Einstein-Hilbert action as a theory of purely cubic interactions
among gravitons and a single auxiliary field. The corresponding equations of
motion are the Einstein field equations rewritten as two coupled first-order
differential equations. Since all Feynman diagrams are cubic, we are able to
derive new off-shell recursion relations for tree-level graviton scattering
amplitudes. With a judicious choice of gauge fixing, we then construct an
especially compact form for the Einstein-Hilbert action in which all graviton
interactions are simply proportional to the graviton kinetic term. Our results
apply to graviton perturbations about an arbitrary curved background spacetime.Comment: 20 pages, 1 figur
Quantum Gravity Constraints from Unitarity and Analyticity
We derive rigorous bounds on corrections to Einstein gravity using unitarity
and analyticity of graviton scattering amplitudes. In spacetime
dimensions, these consistency conditions mandate positive coefficients for
certain quartic curvature operators. We systematically enumerate all such
positivity bounds in and before extending to . Afterwards,
we derive positivity bounds for supersymmetric operators and verify that all of
our constraints are satisfied by weakly-coupled string theories. Among
quadratic curvature operators, we find that the Gauss-Bonnet term in
is inconsistent unless new degrees of freedom enter at the natural cutoff scale
defined by the effective theory. Our bounds apply to perturbative ultraviolet
completions of gravity.Comment: 26 page
Proof of the Weak Gravity Conjecture from Black Hole Entropy
We prove that higher-dimension operators contribute positively to the entropy
of a thermodynamically stable black hole at fixed mass and charge. Our results
apply whenever the dominant corrections originate at tree level from quantum
field theoretic dynamics. More generally, positivity of the entropy shift is
equivalent to a certain inequality relating the free energies of black holes.
These entropy inequalities mandate new positivity bounds on the coefficients of
higher-dimension operators. One of these conditions implies that the
charge-to-mass ratio of an extremal black hole asymptotes to unity from above
for increasing mass. Consequently, large extremal black holes are unstable to
decay to smaller extremal black holes and the weak gravity conjecture is
automatically satisfied. Our findings generalize to arbitrary spacetime
dimension and to the case of multiple gauge fields. The assumptions of this
proof are valid across a range of scenarios, including string theory
constructions with a dilaton stabilized below the string scale.Comment: 35 pages, 2 figure
Clinical Presentation and Treatment Outcomes of Children and Adolescents with Low Back Pain in Physical Therapy
Purpose: Low back pain (LBP) is a common condition in adolescents, and a specific pathoanatomical origin for the symptoms cannot always be determined. The purpose of this work was to examine the clinical presentation and outcomes of rehabilitation for adolescents with LBP. Methods: This study was completed in three phases. Phase 1 was a retrospective review of 25 patients under the age of 18 who were seen for treatment of LBP. Information regarding the patients' diagnoses, history, examination, and outcome were collected from chart review. Phase 2 was a review of 99 patients under the age of 18 with LBP. Numerical Pain Rating Scale (NPRS) and the Modified Oswestry Questionnaire (OSW) were recorded. Phase 3 consisted of a prospective study of treatment-based classification (TBC) of 34 adolescent patients seen in physical therapy for LBP. Treatment duration and content were at the clinician's discretion. Patients completed an OSW and NPRS before and after physical therapy. Patients were classified using a TBC algorithm, and effectiveness of classification on outcome was examined. Results: In study 1, initial pain scores were lower if a specific pathology was present (P=.001). Initial pain and OSW scores were poorly correlated (r= 0.16). 44% (n=11) of patients scored under the floor value of 12% on OSW. A second examination of the OSW in study 2 concluded that OSW was moderately correlated with NPRS (0.59). Chronbach's alpha was 0.86. All 10 items in OSW appeared to load onto two latent factors. In study 3, a classification decision was able to be made with a moderate degree of reliability (0.53 (0.28, 0.79) ≤ κ ≤ 0.89 (.74, 1.0)) in all of the 34 patients. Stabilization was the most commonly prescribed treatment by clinicians. Those who were matched to their TBC classification experienced fewer numbers of visits than those who were not. Conclusions: It appears the OSW is a valid and reliable tool for assessing clinical outcome of physical therapy intervention for adolescents with LBP. These results also suggest that a TBC approach to treatment of LBP in this population may be effective for improvements in clinical outcome
Using The Exponentially Weighted Moving Average Mean Chart For Change Point Analysis
The exponentially weighted moving average (EWMA) chart X for monitoring a pro-cess mean was introduced by Roberts (1959)[1]. Various authors have studied thischart. Shamma and Shamma (1992)[19] introduced an EWMA of an EWMA chart,referred to as the double EWMA chart. Since then the EWMA of the EWMA ofthe EWMA (triple EWMA) chart and the EWMA of the EWMA of the EWMAof the EWMA (quadruple EWMA) charts have been introduced into the literature.Their claims are that the double EWMA X chart outperformed the EWMA chartfor the monitoring the process mean. Further it was claimed that the triple EWMAX chart outperformed the double EWMA X chart and the quadruple EWMA chartoutperformed the triple EWMA X chart. We demonstrate that an EWMA X chartcan be designed that outperforms the double EWMA X chart. We show this usingsimulation. The EWMA X has been used to predict the change point. We providea method using the likelihood function to predict the change point. A comparison ismade with the Shewhart X chart
Three Little Chestnuts (A Tragedy In Still Life)
https://digitalcommons.library.umaine.edu/mmb-vp/6428/thumbnail.jp
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