One- and two-dimensional higher-point conformal blocks as free-particle wavefunctions in AdS3⊗m_3^{\otimes m}

We establish that all of the one- and two-dimensional global conformal blocks are, up to some choice of prefactor, free-particle wavefunctions in tensor products of AdS$_3$ or limits thereof. Our first core observation is that the six-point comb-channel conformal blocks correspond to free-particle wavefunctions on an AdS$_3$ constructed directly in cross-ratio space. This construction generalizes to blocks for a special class of diagrams, which are determined as free-particle wavefunctions in tensor products of AdS$_3$. Conformal blocks for all the remaining topologies are obtained as limits of the free wavefunctions mentioned above. Our results show directly that the integrable models associated with all one- and two-dimensional conformal blocks can be seen as limits of free theory, and manifest a relation between AdS and CFT kinematics that lies outside of the standard AdS/CFT dictionary. We complete the discussion by providing explicit Feynman-like rules that can be used to work out blocks for all topologies, as well as a Mathematica notebook that allows simple computation of Casimir equations and series expansions for blocks, by requiring just an OPE diagram as input.Comment: 39 pages + an appendix, 18 figures, Mathematica notebook attache

Feynman Rules for Scalar Conformal Blocks

We complete the proof of "Feynman rules" for constructing $M$-point conformal blocks with external and internal scalars in any topology for arbitrary $M$ in any spacetime dimension by combining the rules for the blocks (based on their Witten diagram interpretation) with the rules for the construction of conformal cross ratios (based on OPE flow diagrams). The full set of Feynman rules leads to blocks as power series of the hypergeometric type in the conformal cross ratios. We then provide a proof by recursion of the Feynman rules which relies heavily on the first Barnes lemma and the decomposition of the topology of interest in comb-like structures. Finally, we provide a nine-point example to illustrate the rules.Comment: 61 pages + an appendi

Health-related quality of life among general practice patients with differing chronic diseases in Germany: Cross sectional survey

Background This study was carried out to compare the HRQoL of patients in general practice with differing chronic diseases with the HRQoL of patients without chronic conditions, to evaluate the HRQoL of general practice patients in Germany compared with the HRQoL of the general population, and to explore the influence of different chronic diseases on patients HRQoL, independently of the effects of multiple confounding variables. Methods A cross-sectional questionnaire survey including the SF-36, the EQ-5D and demographic questions was conducted in 20 general practices in Germany. 1009 consecutive patients aged 15–89 participated. The SF-36 scale scores of general practice patients with differing chronic diseases were compared with those of patients without chronic conditions. Differences in the SF-36 scale/summary scores and proportions in the EQ-5D dimensions between patients and the general population were analyzed. Independent effects of chronic conditions and demographic variables on the HRQoL were analyzed using multivariable linear regression and polynomial regression models. Results The HRQoL for general practice patients with differing chronic diseases tended to show more physical than mental health impairments compared with the reference group of patients without. Patients in general practice in Germany had considerably lower SF-36 scores than the general population (P < 0.001 for all) and showed significantly higher proportions of problems in all EQ-5D dimensions except for the self-care dimension (P < 0.001 for all). The mean EQ VAS for general practice patients was lower than that for the general population (69.2 versus 77.4, P < 0.001). The HRQoL for general practice patients in Germany seemed to be more strongly affected by diseases like depression, back pain, OA of the knee, and cancer than by hypertension and diabetes. Conclusion General practice patients with differing chronic diseases in Germany had impaired quality of life, especially in terms of physical health. The independent impacts on the HRQoL were different depending on the type of chronic disease. Findings from this study might help health professionals to concern more influential diseases in primary care from the patient´s perspective

The a-theorem and conformal symmetry breaking in holographic RG flows

We study holographic models describing an RG flow between two fixed points driven by a relevant scalar operator. We show how to introduce a spurion field to restore Weyl invariance and compute the anomalous contribution to the generating functional in even dimensional theories. We find that the coefficient of the anomalous term is proportional to the difference of the conformal anomalies of the UV and IR fixed points, as expected from anomaly matching arguments in field theory. For any even dimensions the coefficient is positive as implied by the holographic a-theorem. For flows corresponding to spontaneous breaking of conformal invariance, we also compute the two-point functions of the energy-momentum tensor and the scalar operator and identify the dilaton mode. Surprisingly we find that in the simplest models with just one scalar field there is no dilaton pole in the two-point function of the scalar operator but a stronger singularity. We discuss the possible implications.Comment: 50 pages. v2: minor changes, added references, extended discussion. v3: we have clarified some of the calculations and assumptions, results unchanged. v4: published version in JHE

Intraocular lenses in age-related macular degeneration

Purpose: The aim of this work is to review the lenses, assessing their advantages and disadvantages. We describe a total of seven types of intraocular lenses (IOLs) recommended for age-related macular degeneration (AMD). Methods: We used the PubMed web platform to search for implantable devices in various stages of AMD. We searched for both prospective and retrospective studies and also case reports. Results: Clinical results in AMD patients have been described for a total of seven types of IOLs recommended for AMD: an implantable miniature telescope (IMT), IOL-VIP System, Lipshitz macular implant (LMI), sulcus-implanted Lipshitz macular implant, LMI-SI, Fresnel Prism Intraocular Lens, iolAMD and Scharioth Macula Lens. Conclusions: We conclude that to objectively ascertain the effectiveness and safety of these lenses, further independent clinical studies with longer follow-up data are necessary prior to the general use of these optical devices