Harmonic R matrices for scattering amplitudes and spectral regularization

Planar N=4 supersymmetric Yang-Mills theory appears to be integrable. While this allows one to find this theory's exact spectrum, integrability has hitherto been of no direct use for scattering amplitudes. To remedy this, we deform all scattering amplitudes by a spectral parameter. The deformed tree-level four-point function turns out to be essentially the one-loop R matrix of the integrable N=4 spin chain satisfying the Yang-Baxter equation. Deformed on-shell three-point functions yield novel three-leg R matrices satisfying bootstrap equations. Finally, we supply initial evidence that the spectral parameter might find its use as a novel symmetry-respecting regulator replacing dimensional regularization. Its physical meaning is a local deformation of particle helicity, a fact which might be useful for a much larger class of nonintegrable four-dimensional field theories. © 2013 American Physical Society

Spectral parameters for scattering amplitudes in N=4 super Yang-Mills theory

Planar N= 4 Super Yang-Mills theory appears to be a quantum integrable four-dimensional conformal theory. This has been used to find equations believed to describe its exact spectrum of anomalous dimensions. Integrability seemingly also extends to the planar space-time scattering amplitudes of the N= 4 model, which show strong signs of Yangian invariance. However, in contradistinction to the spectral problem, this has not yet led to equations determining the exact amplitudes. We propose that the missing element is the spectral parameter, ubiquitous in integrable models. We show that it may indeed be included into recent on-shell approaches to scattering amplitude integrands, providing a natural deformation of the latter. Under some constraints, Yangian symmetry is preserved. Finally we speculate that the spectral parameter might also be the regulator of choice for controlling the infrared divergences appearing when integrating the integrands in exactly four dimensions. © 2014 The Author(s)

The electrode potential in modelling of transport processes in aqueous electrolytes

In the paper equations of mathematical model of mechanical, heat, diffusion and electromagnetic processes in aqueous nonpolarized solutions of electrolyte with use of electrode potential are formulated. It is shown that under certain conditions new coupled parameters can be found: absolute temperature — entropy density, pressure — specific volume, chemical potential — concentration of anions, electrode potential — mass electric charge density. It enables to relate balance model equations with Maxwell equations.У роботі отримано вихідні співвідношення математичної моделі механічних, теплових, дифузійних та електромагнітних процесів у водних неполяризовних розчинах електроліту з використанням електродного потенціалу. Параметрами локального стану розчину вибрано абсолютну температуру — масову густину ентропії, тиск — питомий об’єм, хімічні потенціали — концентрації компонент. Показано, що з використанням масової густини електричного заряду компонент (катіонів і аніонів) та умови нормування концентрацій, можна визначити нові спряжені параметри, а саме: узагальнений хімічний потенціал — концентрацію аніонів та електродний потенціал — масову густину електричного заряду середовища. Введення масової густини електричного заряду середовища у простір параметрів стану дозволяє визначити прямий зв’язок відповідних рівнянь стану та балансових співвідношень із рівнянням Максвелла. Виходячи з потенціальності внутрішньої енергії (вільної енергії Гельмгольца), із сформульованих рівнянь Гіббса й Ейлера отримано лінійні рівняння стану. Закони збереження та балансові рівняння моделі записано для густини маси, концентрації аніонів, масової густини електричного заряду середовища, імпульсу й ентропії. З цих рівнянь, використовуючи кінетичні рівняння та рівняння стану, одержано розв’язуючу систему рівнянь моделі. Сформульовано відповідні початкові та граничні умови.В работе получены исходные соотношения математической модели механических, тепловых, диффузионных и электромагнитных процессов в водных растворах электролитов с использованием электродного потенциала без учета поляризации среды. В качестве параметров, характеризующих локальное состояние раствора, выбраны абсолютная температура — массовая плотность энтропии, давление — удельный объем, химические потенциалы — концентрации компонент. Показано, что, используя массовые плотности электрических зарядов компонент (катионов и анионов) и условия нормирования концентраций можно ввести новые сопряженные параметры: обобщенный химический потенциал — концентрацию анионов и электродный потенциал — массовую плотность электрического заряда среды. Использование в качества параметра состояния массовой плотности электрического заряда среды позволяет установить непосредственную связь соответствующих уравнений состояния и балансовых соотношений с уравнениями Максвелла. Исходя из потенциальности внутренней энергии (свободной энергии Гельмгольца) из сформулированных уравнений Гиббса и Эйлера получены линейные уравнения состояния. Законы сохранения и балансовые уравнения модели записаны для плотности массы, концентрации анионов, массовой плотности электрического заряда среды, импульса и энтропии. Из этих уравнений, используя кинетические уравнения и уравнения состояния, получена разрешающая система уравнений модели. Сформулированы соответствующие начальные и граничные условия

Tree-level scattering amplitudes from the amplituhedron

7 pages, 2 figures, to be published in the Journal of Physics: Conference Series. Proceedings for the "7th Young Researcher Meeting", Torino, 2016A central problem in quantum field theory is the computation of scattering amplitudes. However, traditional methods are impractical to calculate high order phenomenologically relevant observables. Building on a few decades of astonishing progress in developing non-standard computational techniques, it has been recently conjectured that amplitudes in planar N=4 super Yang-Mills are given by the volume of the (dual) amplituhedron. After providing an introduction to the subject at tree-level, we discuss a special class of differential equations obeyed by the corresponding volume forms. In particular, we show how they fix completely the amplituhedron volume for next-to-maximally helicity violating scattering amplitudes.Peer reviewe

Contribution to a ranking procedure for polymeric caotings and hydrophobic agents for concrete

One of the possible ways to protect the concrete is using coatings and hydrophobic agents that act as a barrier against the environment. When selecting the material for concrete protection, importance should be given to these properties of diffusion and permeability. The coatings and the hydrophobic agents must stop the penetration of water and delay the influence of aggressive agents, allowing the structure to breathe by a water vapour diffusion mechanism. An evaluation of the surface layer transport properties gives information on the durability of a particular concrete. In order to make the selection of coatings and hydrophobic agents for concrete protection, it is important to analyse the compound’s technical and economical performances. A ranking procedure, developed by Czarnecki and Lukowski, is applied on a series of concrete protection products. The ranking procedure is applied to evaluate durability experiments, carried out on some commercially available silicone, acrylic and epoxy compounds for surface treatment of concrete. The ranking procedure transforms experimental data of properties into one numerical value, by which the products can be classified according to the way on which their properties present an optimised or even best buy combination. The paper shows the use of the ranking procedure methodology, and points at the importance of the choice of the criteria and of their relative weight factor in the evaluation. The method is a valuable tool for the ranking of similar materials, whose performance is based on the same or similar physical or chemical processes

Ferrets exclusively synthesize Neu5Ac and express naturally humanized influenza A virus receptors

Mammals express the sialic acids ​N-acetylneuraminic acid (​Neu5Ac) and ​N-glycolylneuraminic acid (​Neu5Gc) on cell surfaces, where they act as receptors for pathogens, including influenza A virus (IAV). ​Neu5Gc is synthesized from ​Neu5Ac by the enzyme cytidine monophosphate-N-acetylneuraminic acid hydroxylase (CMAH). In humans, this enzyme is inactive and only ​Neu5Ac is produced. Ferrets are susceptible to human-adapted IAV strains and have been the dominant animal model for IAV studies. Here we show that ferrets, like humans, do not synthesize ​Neu5Gc. Genomic analysis reveals an ancient, nine-exon deletion in the ferret CMAH gene that is shared by the Pinnipedia and Musteloidia members of the Carnivora. Interactions between two human strains of IAV with the sialyllactose receptor (sialic acid—α2,6Gal) confirm that the type of terminal sialic acid contributes significantly to IAV receptor specificity. Our results indicate that exclusive expression of ​Neu5Ac contributes to the susceptibility of ferrets to human-adapted IAV strains

Twist operators in N=4 beta-deformed theory

In this paper we derive both the leading order finite size corrections for twist-2 and twist-3 operators and the next-to-leading order finite-size correction for twist-2 operators in beta-deformed SYM theory. The obtained results respect the principle of maximum transcendentality as well as reciprocity. We also find that both wrapping corrections go to zero in the large spin limit. Moreover, for twist-2 operators we studied the pole structure and compared it against leading BFKL predictions.Comment: 17 pages; v2: minor changes, references adde

Angular and Temperature Tuning of Emission from Vertical-External-Cavity Surface-Emitting Lasers (VECSELs)

In this paper we demonstrate how the tuning of the VECSEL heterostructure can be precisely determined. Since the VECSEL active region is embodied in a microcavity, the photoluminescence signal collected from the chip surface is modified by the resonance of this cavity. The angle resolved photoluminescence measurements combined with the temperature tuning of the structure allowed us to precisely determine VECSEL emission features. The investigated structure consists of GaAs cavity with six InGaAs quantum wells and is designed for lasing at 980 nm. Introduction Vertical-external-cavity surface-emitting lasers (VECSELs

Six and seven loop Konishi from Luscher corrections

In the present paper we derive six and seven loop formulas for the anomalous dimension of the Konishi operator in N=4 SYM from string theory using the technique of Luscher corrections. We derive analytically the integrand using the worldsheet S-matrix and evaluate the resulting integral and infinite sum using a combination of high precision numerical integration and asymptotic expansion. We use this high precision numerical result to fit the integer coefficients of zeta values in the final analytical answer. The presented six and seven loop results can be used as a cross-check with FiNLIE on the string theory side, or with direct gauge theory computations. The seven loop level is the theoretical limit of this Luscher approach as at eight loops double-wrapping corrections will appear.Comment: 18 pages, typos correcte

The Bajnok-Janik formula and wrapping corrections

We write down the simplified TBA equations of the $AdS_5 \times S^5$ string sigma-model for minimal energy twist-two operators in the sl(2) sector of the model. By using the linearized version of these TBA equations it is shown that the wrapping corrected Bethe equations for these states are identical, up to O(g^8), to the Bethe equations calculated in the generalized L\"uscher approach (Bajnok-Janik formula). Applications of the Bajnok-Janik formula to relativistic integrable models, the nonlinear O(n) sigma models for n=2,3,4 and the SU(n) principal sigma models, are also discussed.Comment: Latex, 22 pages, published versio