Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

We show that scattering amplitudes in planar N = 4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes' theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L + 4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. Finally, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.Comment: 104 pages, six awesome figures and ancillary files containing the results in Mathematica forma

Mobility of O2−_2^- ions in supercritical Ar: Experiment and Molecular Dynamics Simulations

A new analysis and new Molecular Dynamics (MD) simulations of the measurements of the mobility $\mu_{i}$ of O$_{2}^{-}$ ions in dense supercritical Ar gas are reported. $\mu_{i}$ shows a marked dependence on the distance from the critical temperature $T_{c}.$ A mobility defect appears as a function of the gas density and its maximum value occurs below the critical density. The locus of points of maximum mobility defect in the $P-T$ plane appears on the extrapolation of the coexistence curve into the single-phase region. MD simulations quantitatively reproduce the mobility defect near $T_{c}.$Comment: 7 pages, 6 figures, submitted to International Journal of Mass Spectrometry, issue in honor of E. Illenberge

The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM

We provide an analytic formula for the (rescaled) one-loop scalar hexagon integral $\tilde\Phi_6$ with all external legs massless, in terms of classical polylogarithms. We show that this integral is closely connected to two integrals appearing in one- and two-loop amplitudes in planar $\\mathcal{N}=4$ super-Yang-Mills theory, $\Omega^{(1)}$ and $\Omega^{(2)}$. The derivative of $\Omega^{(2)}$ with respect to one of the conformal invariants yields $\tilde\Phi_6$, while another first-order differential operator applied to $\tilde\Phi_6$ yields $\Omega^{(1)}$. We also introduce some kinematic variables that rationalize the arguments of the polylogarithms, making it easy to verify the latter differential equation. We also give a further example of a six-dimensional integral relevant for amplitudes in $\\mathcal{N}=4$ super-Yang-Mills.Comment: 18 pages, 2 figure

Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills

Scattering amplitudes in superconformal field theories do not enjoy this symmetry, because the definition of asymptotic states involve a notion of infinity. Concentrating on planar $\mathcal{N}=4$ Yang-Mills, we consider a generalization of scattering amplitudes which depends on twice as many Grassmann variables. We conjecture that it restores at least half of the superconformal symmetries, and all of the dual superconformal symmetries. The object arises naturally as the dual of a null polygonal Wilson loop in an $(x,\theta,\bar\theta)$ superspace. We support the conjecture by using it to obtain the total differential of all $n$-point two-loop MHV amplitudes, and showing that the result passes consistency checks. Potential all-loop constraints are also discussed.Comment: 25 pages, 2 figures and 1 noteboo

Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory

We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behaviour, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral \Omega^{(2)}, also plays a key role in a new representation of the remainder function R_6^{(2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) \times (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) \times (parity even) part. The second non-polylogarithmic function, the loop integral \tilde{\Omega}^{(2)}, characterizes this sector. Both \Omega^{(2)} and tilde{\Omega}^{(2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.Comment: 51 pages, 4 figures, one auxiliary file with symbols; v2 minor typo correction

Adipose tissue hyaluronan production improves systemic glucose homeostasis and primes adipocytes for CL 316,243-stimulated lipolysis

Plasma hyaluronan (HA) increases systemically in type 2 diabetes (T2D) and the HA synthesis inhibitor, 4-Methylumbelliferone, has been proposed to treat the disease. However, HA is also implicated in normal physiology. Therefore, we generated a Hyaluronan Synthase 2 transgenic mouse line, driven by a tet-response element promoter to understand the role of HA in systemic metabolism. To our surprise, adipocyte-specific overproduction of HA leads to smaller adipocytes and protects mice from high-fat-high-sucrose-diet-induced obesity and glucose intolerance. Adipocytes also have more free glycerol that can be released upon beta3 adrenergic stimulation. Improvements in glucose tolerance were not linked to increased plasma HA. Instead, an HA-driven systemic substrate redistribution and adipose tissue-liver crosstalk contributes to the systemic glucose improvements. In summary, we demonstrate an unexpected improvement in glucose metabolism as a consequence of HA overproduction in adipose tissue, which argues against the use of systemic HA synthesis inhibitors to treat obesity and T2D

Republicanism and Markets

The republican tradition has long been ambivalent about markets and commercial society more generally: from the contrasting positions of Rousseau and Smith in the eighteenth century to recent neorepublican debates about capitalism, republicans have staked out diverse positions on fundamental issues of political economy. Rather than offering a systematic historical survey of these discussions, this chapter will instead focus on the leading neo-republican theory—that of Philip Pettit—and consider its implications for market society. As I will argue, Pettit’s theory is even friendlier to markets than most have believed: far from condemning commercial society, his theory recognizes that competitive markets and their institutional preconditions are an alternative means to limit arbitrary power across the domestic, economic, and even political spheres. While most republican theorists have focused on political means to limit such power—including both constitutional means (e.g., separation of powers, judicial review, the rule of law, federalism) and participatory ones (democratic elections and oversight)—I will examine here an economic model of republicanism that can complement, substitute for, and at times displace the standard political model. Whether we look at spousal markets, labor markets, or residential markets within federal systems, state policies that heighten competition among their participants and resource exit from abusive relationships within them can advance freedom as non-domination as effectively or even more effectively than social-democratic approaches that have recently gained enthusiasts among republicans. These conclusions suggest that democracy, be it social or political, is just one means among others for restraining arbitrary power and is consequently less central to (certain versions of) republicanism than we may have expected. So long as they counteract domination, economic inroads into notionally democratic territory are no more worrisome than constitutional ones

Cut Diagrams for High Energy Scatterings

A new approach is introduced to study QCD amplitudes at high energy and comparatively small momentum transfer. Novel cut diagrams, representing resummation of Feynman diagrams, are used to simplify calculation and to avoid delicate cancellations encountered in the usual approach. Explicit calculation to the 6th order is carried out to demonstrate the advantage of cut diagrams over Feynman diagrams.Comment: uu-encoded file containing a latex manuscript with 14 postscript figure