Planar N=4 gauge theory and the Inozemtsev long range spin chain

We investigate whether the (planar, two complex scalar) dilatation operator of N=4 gauge theory can be, perturbatively and, perhaps, non-perturbatively, described by an integrable long range spin chain with elliptic exchange interaction. Such a chain was introduced some time ago by Inozemtsev. In the limit of sufficiently ``long'' operators a Bethe ansatz exists, which we apply at the perturbative two- and three-loop level. Spectacular agreement is found with spinning string predictions of Frolov and Tseytlin for the two-loop energies of certain large charge operators. However, we then go on to show that the agreement between perturbative gauge theory and semi-classical string theory begins to break down, in a subtle fashion, at the three-loop level. This corroborates a recently found disagreement between three-loop gauge theory and near plane-wave string theory results, and quantitatively explains a previously obtained puzzling deviation between the string proposal and a numerical extrapolation of finite size three-loop anomalous dimensions. At four loops and beyond, we find that the Inozemtsev chain exhibits a generic breakdown of perturbative BMN scaling. However, our proposal is not necessarily limited to perturbation theory, and one would hope that the string theory results can be recovered from the Inozemtsev chain at strong 't Hooft coupling.Comment: 31 pages, no figure; v1: one reference added, minor changes; v2: slightly extended discussion of rapidity, references adde

Optimal control of time-dependent targets

In this work, we investigate how and to which extent a quantum system can be driven along a prescribed path in Hilbert space by a suitably shaped laser pulse. To calculate the optimal, i.e., the variationally best pulse, a properly defined functional is maximized. This leads to a monotonically convergent algorithm which is computationally not more expensive than the standard optimal-control techniques to push a system, without specifying the path, from a given initial to a given final state. The method is successfully applied to drive the time-dependent density along a given trajectory in real space and to control the time-dependent occupation numbers of a two-level system and of a one-dimensional model for the hydrogen atom.Comment: less typo

The Muddle of the 'Westminster Model': A Concept Stretched Beyond Repair

The term ‘Westminster model’, widely used in both the academic and practitioner literatures, is a familiar one. But detailed examination finds significant confusion about its meaning. This article follows Giovanni Sartori's advice for ‘reconstructing’ a social science term whose meaning may be unclear through review of its use in the recent literature. It finds that many authors in comparative politics use the term ‘Westminster model’ without definition, while those providing definitions associate it with a large (and sometimes conflicting) set of attributes, and a set of countries often not demonstrating those attributes. Some have sought to respect this diversity by proposing variants like ‘Washminster’ or ‘Eastminster’, while others suggest that the term should be seen as a loose ‘family resemblance’ concept. But on examination it no longer meets even the – relatively weak – requirements for family resemblance. To end the muddle, and the risk of flawed inferences and false generalization, comparative scholars should drop this term, and select cases based on more precise attributes instead

Why it Is Indeed Time for the Westminster Model to Be Retired from Comparative Politics

The term ‘Westminster model’ is frequently used by political scientists and practitioners. But our recent examination (Russell and Serban 2021), published in this journal, uncovered wide variation in how it is defined – demonstrating that it is more ‘muddle’ than ‘model’. This sparked a response article from Flinders et al. (2021), which we in turn respond to in this piece. We briefly revisit our initial research questions, methodology and findings, before reflecting on their analysis. We emphasize that, notwithstanding the critics’ negative tone, we and they agree on certain fundamentals. In particular on our original central point, that the ‘Westminster model’ is an ill-defined term with a long history, which mostly makes it unsuited to positivist comparative political science research. While the ‘Westminster model’ may have some valid vestigial uses, within the UK political system, or as an object of study for interpretivist political science, it does not provide a rigorous basis for case selection and comparative political science analysis

Strong coupling from the Hubbard model

It was recently observed that the one dimensional half-filled Hubbard model reproduces the known part of the perturbative spectrum of planar N=4 super Yang-Mills in the SU(2) sector. Assuming that this identification is valid beyond perturbation theory, we investigate the behavior of this spectrum as the 't Hooft parameter \lambda becomes large. We show that the full dimension \Delta of the Konishi superpartner is the solution of a sixth order polynomial while \Delta for a bare dimension 5 operator is the solution of a cubic. In both cases the equations can be solved easily as a series expansion for both small and large \lambda and the equations can be inverted to express \lambda as an explicit function of \Delta. We then consider more general operators and show how \Delta depends on \lambda in the strong coupling limit. We are also able to distinguish those states in the Hubbard model which correspond to the gauge invariant operators for all values of \lambda. Finally, we compare our results with known results for strings on AdS_5\times S^5, where we find agreement for a range of R-charges.Comment: 14 pages; v2: 17 pages, 2 figures, appendix and references added; typos fixed, minor changes; v3 fixed figures; v4 more references added, minor correctio

The Effects of Cinnamon Supplementation on Plasma Lipid Concentrations: A Systematic Review and Meta-Analysis

Background: Cinnamon is a rich botanical source of polyphenols, whose positive effects on blood lipid concentrations have been hypothesized, but have not been conclusively studied. Objective: To systematically review and evaluate the effect of administration of cinnamon on blood lipid concentrations. Methods: We assessed 13 RCTs with 750 participants investigating the effect of cinnamon supplementation on blood lipid concentrations. A meta-analysis was performed using randomeffect models, with weighted mean differences (with 95% CI) for endpoints calculated using a random-effects model. Results: No statistically significant effect of cinnamon was observed on blood LDL-C (WMD: - 0.16 mmol/L [-6.19 mg/dL], 95% CI: -0.35, 0.03 [-13.53, 1.16], p = 0.10) and HDL-C (WMD: 0.05 mmol/L [1.92 mg/dL], 95% CI: -0.03, 0.12 [-0.03, 4.64], p = 0.21) concentrations. However, a statistically significant reduction in blood triglycerides (WMD: -0.27 mmol/L [- 23.91 mg/dL], 95% CI: -0.39, -0.14 [-34.54, -12.40], p < 0.01) and total cholesterol concentrations (WMD: -0.36 mmol/L [-13.92 mg/dL], 95% CI: -0.63, -0.09 [-24.36, -3.48], p < 0.01) was observed. HDL-C was significantly elevated following the omission of one study (WMD: 0.04 mmol/L [1.54 mg/dL], 95% CI: 0.03, 0.06 [1.16, 2.32], p < 0.01) during our sensitivity analysis. A meta-regression analysis was conducted and no significant association was found between changes in lipid parameters and cinnamon dose. In contrast, changes in blood levels of total cholesterol (slope: 0.09; 95% CI: 0.02, 0.16; p < 0.01), LDL-C (slope: 0.05; 95% CI: 0.001, 0.10; p = 0.05) and triglycerides (slope: 0.06; 95% CI: 0.04, 0.09; p < 0.01) were significantly and positively associated with the duration of supplementation. No statistically significant association was found between blood HDL-C changes and duration of supplementation. Conclusion: Cinnamon supplementation significantly reduced blood triglycerides and total cholesterol concentrations without any significant effect on LDL-C and HDL-C