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

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

A heuristic approach for multiple restricted multiplication

Published versio

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

Deep optical imaging of AGB circumstellar envelopes

We report results of a program to image the extended circumstellar envelopes of asymptotic giant branch (AGB) stars in dust-scattered Galactic light. The goal is to characterize the shapes of the envelopes to probe the mass-loss geometry and the presence of hidden binary companions. The observations consist of deep optical imaging of 22 AGB stars with high mass loss rates: 16 with the ESO 3.5 m NTT telescope, and the remainder with other telescopes. The circumstellar envelopes are detected in 15 objects, with mass loss rates > 2E-6 Msun/year. The surface brightness of the envelopes shows a strong decrease with Galactic radius, which indicates a steep radial gradient in the interstellar radiation field. The envelopes range from circular to elliptical in shape, and we characterize them by the ellipticity (E = major/minor axis) of iso-intensity contours. We find that about 50 percent of the envelopes are close to circular with E 1.2. We interpret the shapes in terms of populations of single stars and binaries whose envelopes are flattened by a companion. The distribution of E is qualitatively consistent with expectations based on population synthesis models of binary AGB stars. We also find that about 50 percent of the sample exhibit small-scale, elongated features in the central regions. We interpret these as the escape of light from the central star through polar holes, which are also likely produced by companions. Our observations of envelope flattening and polar holes point to a hidden population of companions within the circumstellar envelopes of AGB stars. These companions are expected to play an important role in the transition to post-AGB stars and the formation of planetary nebulae.Comment: 19 pages, 13 figures, color pictures in Appendix, accepted by A&

Successful islet allotransplantation in diabetic rats immunosuppressed with FK506: A functional and immunological study

The effect of a novel immunosuppressive agent, FK506, on fresh islet allografts was evaluated in diabetic rats across major histocompatibility complex (MHC) barriers with respect to the transplantation (TR) site, islet source, treatment regimen, and antidonor antibody (Ab) titers of the recipients after TR. The functional periods of Wistar (Wi) islets transplanted under kidney capsule (KC) or intraportally (IPo) and of a mixture of Wi and Lewis (Le) islets under KC or IPo in nonimmunosuppressed ACI rat recipients were 6.9 ± 0.4 (n = 7), 6.4 ± 0.5 (n = 7), 5.6 ± 0.4 (n = 7), and 6.2 ± 0.4 (n = 5) days, respectively. FK506 treatment at 1 mg/kg/d intramuscularly (IM) for 2 weeks (protocol I) following islet TR under KC and IPo significantly prolonged the allograft function to more than 71.8 ± 11.3 (n = 10) and 161.7 ± 18.6 (n = 11) days, respectively. Additional treatment with FK506 at 1 mg/kg/wk (protocol II) further increased the islet survival under KC to more than 212.6 ± 22.3 (n = 8) days. With this FK506 treatment protocol, the Wi + Le mixed-islet allograft function was extended to more than 106.1 ± 10.5 (n = 7) and 167.9 ± 28.6 (n = 7) days under KC and IPo, respectively. Nephrectomy in 8 8 ACI rats with long-term-functioning Wi (n = 6) and Wi + Le (n = 2) islet allografts resulted in their return to hyperglycemia. Immunohistochemical staining showed abundant insulin-positive cells at the graft site, with small numbers of CD4- and CD8-positive cells present in the vicinity of the normal-appearing islets. Macrophages were not detected. The immunosuppressive effect of FK506 was further tested in ACI rats presensitized by a previous Wi islet TR. When the duration between the first and second TR under KC was 114.3 ± 20.5 days, protocol II treatment significantly prolonged the graft function to more than 152.9 ± 28.7 (n = 8) days. However, with a short duration of about 2 weeks between the two TRs, the same FK506 protocol achieved islet graft function of 14.0 ± 3.8 days (n = 7). Additional immunosuppression with cyclophosphamide did not further improve the survival time. Antidonor Abs detected in ACI recipients of Wi islet allografts were significantly lower in the FK506-treated animals compared with the nontreatment group. Wi and Le skin grafts performed in three ACI rats with long-term-functioning Wi islets IPo caused the rejection of the islet allografts. Skin grafts were also rejected in the first-set fashion. Six ACI recipients with long-term-functioning IPo Wi islet allografts were rendered hyperglycemic by streptozocin (STZ) injection. Long-term normoglycemia without further FK506 immunosuppression was achieved following retransplantation with fresh Wi islets IPo (n = 2), but not under KC (n = 2). The results of the present study indicate that FK506 was an effective immunosuppressant for islet allotransplantation in diabetic ACI rats across MHC barriers with islets from two donor strains, as well as in sensitized recipients whose antidonor activities had subsided. The efficacy of the immunosuppression was influenced by the FK506 treatment protocol and the site of the islet transplant. The results suggest that FK506 could be useful in clinical islet TR. © 1994

MeV ion scattering from thin Si single crystals: A novel approach to interface studies

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