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 $q$ and mass $m$ such that $q \geq m/m_{\rm Pl}$. 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 $q/m$) and those that do not (parameterized by a coefficient $\gamma$). Infrared consistency implies that $q/m$ is bounded from below for small $\gamma$.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 $D\geq 4$ spacetime dimensions, these consistency conditions mandate positive coefficients for certain quartic curvature operators. We systematically enumerate all such positivity bounds in $D=4$ and $D=5$ before extending to $D\geq 6$. 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 $D\geq 5$ 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

Twofold Symmetries of the Pure Gravity Action

We recast the action of pure gravity into a form that is invariant under a twofold Lorentz symmetry. To derive this representation, we construct a general parameterization of all theories equivalent to the Einstein-Hilbert action up to a local field redefinition and gauge fixing. We then exploit this freedom to eliminate all interactions except those exhibiting two sets of independently contracted Lorentz indices. The resulting action is local, remarkably simple, and naturally expressed in a field basis analogous to the exponential parameterization of the nonlinear sigma model. The space of twofold Lorentz invariant field redefinitions then generates an infinite class of equivalent representations. By construction, all off-shell Feynman diagrams are twofold Lorentz invariant while all on-shell tree amplitudes are automatically twofold gauge invariant. We extend our results to curved spacetime and calculate the analogue of the Einstein equations. While these twofold invariances are hidden in the canonical approach of graviton perturbation theory, they are naturally expected given the double copy relations for scattering amplitudes in gauge theory and gravity