Taming the ϵ\epsilon-expansion with Large Spin Perturbation Theory

We apply analytic bootstrap techniques to the four-point correlator of fundamental fields in the Wilson-Fisher model. In an $\epsilon$-expansion crossing symmetry fixes the double discontinuity of the correlator in terms of CFT data at lower orders. Large spin perturbation theory, or equivalently the recently proposed Froissart-Gribov inversion integral, then allows one to reconstruct the CFT data of intermediate operators of any spin. We use this method to compute the anomalous dimensions and OPE coefficients of leading twist operators. To cubic order in $\epsilon$ the double discontinuity arises solely from the identity operator and the scalar bilinear operator, making the computation straightforward. At higher orders the double discontinuity receives contributions from infinite towers of higher spin operators. At fourth order, the structure of perturbation theory leads to a proposal in terms of functions of certain degree of transcendentality, which can then be fixed by symmetries. This leads to the full determination of the CFT data for leading twist operators to fourth order.Comment: 16 pages. v2: Added discussion on low spin spectru

An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1/N21/N^2

We apply the methods of modern analytic bootstrap to the critical $O(N)$ model in a $1/N$ expansion. At infinite $N$ the model possesses higher spin symmetry which is weakly broken as we turn on $1/N$. By studying consistency conditions for the correlator of four fundamental fields we derive the CFT-data for all the (broken) currents to order $1/N$, and the CFT-data for the non-singlet currents to order $1/N^2$. To order $1/N$ our results are in perfect agreement with those in the literature. To order $1/N^2$ we reproduce known results for anomalous dimensions and obtain a variety of new results for structure constants, including the global symmetry central charge $C_J$ to this order.Comment: 32 pages + appendices, 2 figures. v2: Improved presentation + new appendix considering mixed correlator. Version to appear in JHE

A comparison between methods of analytical continuation for bosonic functions

In this article we perform a critical assessment of different known methods for the analytical continuation of bosonic functions, namely the maximum entropy method, the non-negative least-square method, the non-negative Tikhonov method, the Pad\'e approximant method, and a stochastic sampling method. Three functions of different shape are investigated, corresponding to three physically relevant scenarios. They include a simple two-pole model function and two flavours of the non-interacting Hubbard model on a square lattice, i.e. a single-orbital metallic system and a two-orbitals insulating system. The effect of numerical noise in the input data on the analytical continuation is discussed in detail. Overall, the stochastic method by Mishchenko et al. [Phys. Rev. B \textbf{62}, 6317 (2000)] is shown to be the most reliable tool for input data whose numerical precision is not known. For high precision input data, this approach is slightly outperformed by the Pad\'e approximant method, which combines a good resolution power with a good numerical stability. Although none of the methods retrieves all features in the spectra in the presence of noise, our analysis provides a useful guideline for obtaining reliable information of the spectral function in cases of practical interest.Comment: 13 pages, 9 figure

Repeated post-exercise administration with a mixture of leucine and glucose alters the plasma amino acid profile in Standardbred trotters

<p>Abstract</p> <p>Background</p> <p>The branched chain amino acid leucine is a potent stimulator of insulin secretion. Used in combination with glucose it can increase the insulin response and the post exercise re-synthesis of glycogen in man. Decreased plasma amino acid concentrations have been reported after intravenous or per oral administration of leucine in man as well as after a single per oral dose in horses. In man, a negative correlation between the insulin response and the concentrations of isoleucine, valine and methionine have been shown but results from horses are lacking. This study aims to determine the effect of repeated per oral administration with a mixture of glucose and leucine on the free amino acid profile and the insulin response in horses after glycogen-depleting exercise.</p> <p>Methods</p> <p>In a crossover design, after a glycogen depleting exercise, twelve Standardbred trotters received either repeated oral boluses of glucose, 1 g/kg body weight (BW) at 0, 2 and 4 h with addition of leucine 0.1 g/kg BW at 0 and 4 h (GLU+LEU), or repeated boluses of water at 0, 2 and 4 h (CON). Blood samples for analysis of glucose, insulin and amino acid concentrations were collected prior to exercise and over a 6 h post-exercise period. A mixed model approach was used for the statistical analyses.</p> <p>Results</p> <p>Plasma leucine, isoleucine, valine, tyrosine and phenylalanine concentrations increased after exercise. Post-exercise serum glucose and plasma insulin response were significantly higher in the GLU+LEU treatment compared to the CON treatment. Plasma leucine concentrations increased after supplementation. During the post-exercise period isoleucine, valine and methionine concentrations decreased in both treatments but were significantly lower in the GLU+LEU treatment. There was no correlation between the insulin response and the response in plasma leucine, isoleucine, valine and methionine.</p> <p>Conclusions</p> <p>Repeated post-exercise administration with a mixture of leucine and glucose caused a marked insulin response and altered the plasma amino acid profile in horses in a similar manner as described in man. However, the decreases seen in plasma amino acids in horses seem to be related more to an effect of leucine and not to the insulin response as seen in man.</p

Rotational averaging-out gravitational sedimentation of colloidal dispersions and phenomena

We report on the differences between colloidal systems left to evolve in the earth's gravitational field and the same systems for which a slow continuous rotation averaged out the effects of particle sedimentation on a distance scale small compared to the particle size. Several systems of micron-sized colloidal particles were studied: a hard sphere fluid, colloids interacting via long-range electrostatic repulsions above the freezing volume fraction, an oppositely charged colloidal system close to either gelation and/or crystallization, colloids with a competing short-range depletion attraction and a long-range electrostatic repulsion, colloidal dipolar chains, and colloidal gold platelets under conditions where they formed stacks. Important differences in the structure formation were observed between the experiments where the particles were allowed to sediment and those where sedimentation was averaged out. For instance, in the case of colloids interacting via long-range electrostatic repulsions, an unusual sequence of dilute-Fluid/dilute-Crystal/dense-Fluid/dense-Crystal phases was observed throughout the suspension under the effect of gravity, related to the volume fraction dependence of the colloidal interactions, whereas the system stayed homogeneously crystallized with rotation. For the oppositely charged colloids, a gel-like structure was found to collapse under the influence of gravity with a few crystalline layers grown on top of the sediment, whereas when the colloidal sedimentation was averaged out, the gel completely transformed into crystallites that were oriented randomly throughout the sample. Rotational averaging out gravitational sedimentation is an effective and cheap way to estimate the importance of gravity for colloidal self-assembly processes.Comment: 13 pages, 13 figure

Third dose of COVID-19 mRNA vaccine closes the gap in immune response between naïve nursing home residents and healthy adults.

peer reviewed[en] BACKGROUND: Nursing home residents, a frail and old population group, respond poorly to primary mRNA COVID-19 vaccination. A third dose has been shown to boost protection against severe disease and death in this immunosenescent population, but limited data is available on the immune responses it induces. METHODS: In this observational cohort study, peak humoral and cellular immune responses were compared 28 days after the second and third doses of the BNT162b2 mRNA COVID-19 vaccine in residents and staff members of two Belgian nursing homes. Only individuals without evidence of previous SARS-CoV-2 infection at third dose administration were included in the study. In addition, an extended cohort of residents and staff members was tested for immune responses to a third vaccine dose and was monitored for vaccine breakthrough infections in the following six months. The trial is registered on ClinicalTrials.gov (NCT04527614). FINDINGS: All included residents (n = 85) and staff members (n = 88) were SARS-CoV-2 infection naïve at third dose administration. Historical blood samples from 28 days post second dose were available from 42 residents and 42 staff members. Magnitude and quality of humoral and cellular immune responses were strongly boosted in residents post third compared to post second dose. Increases were less pronounced in staff members than in residents. At 28 days post third dose, differences between residents and staff had become mostly insignificant. Humoral, but not cellular, responses induced by a third dose were predictive of subsequent incidence of vaccine breakthrough infection in the six months following vaccination. INTERPRETATION: These data show that a third dose of mRNA COVID-19 vaccine largely closes the gap in humoral and cellular immune response observed after primary vaccination between NH residents and staff members but suggest that further boosting might be needed to achieve optimal protection against variants of concern in this vulnerable population group