Wrapping interactions at strong coupling -- the giant magnon

We derive generalized Luscher formulas for finite size corrections in a theory with a general dispersion relation. For the AdS_5xS^5 superstring these formulas encode leading wrapping interaction effects. We apply the generalized mu-term formula to calculate finite size corrections to the dispersion relation of the giant magnon at strong coupling. The result exactly agrees with the classical string computation of Arutyunov, Frolov and Zamaklar. The agreement involved a Borel resummation of all even loop-orders of the BES/BHL dressing factor thus providing a strong consistency check for the choice of the dressing factor.Comment: 35 pages, 2 figures; v2: comments and references adde

Yangian Symmetry for the Tree Amplituhedron

17 pages, 4 figures; v2: extended discussion of results, minor typos corrected, version published in Journal of Physics ATree-level scattering amplitudes in planar N=4 super Yang-Mills are known to be Yangian-invariant. It has been shown that integrability allows to obtain a general, explicit method to find such invariants. The uplifting of this result to the amplituhedron construction has been an important open problem. In this paper, with the help of methods proper to integrable theories, we successfully fill this gap and clarify the meaning of Yangian invariance for the tree-level amplituhedron. In particular, we construct amplituhedron volume forms from an underlying spin chain. As a by-product of this construction, we also propose a novel on-shell diagrammatics for the amplituhedron.Peer reviewe

A new derivation of Luscher F-term and fluctuations around the giant magnon

15 pages, no figures; v2: added assumption on diagonal scattering and a section on generalizations; v3: minor changes, version accepted for publication in JHEPIn this paper we give a new derivation of the generalized Luscher F-term formula from a summation over quadratic fluctuations around a given soliton. The result is very general providing that S-matrix is diagonal and is valid for arbitrary dispersion relation. We then apply this formalism to compute the leading finite size corrections to the giant magnon dispersion relation coming from quantum fluctuations.Peer reviewe

Five-Loop Anomalous Dimension of Twist-Two Operators

In this article we calculate the five-loop anomalous dimension of twist-two operators in the planar N=4 SYM theory. Firstly, using reciprocity, we derive the contribution of the asymptotic Bethe ansatz. Subsequently, we employ the first finite-size correction for the AdS5xS5 sigma model to determine the wrapping correction. The anomalous dimension found in this way passes all known tests provided by the NLO BFKL equation and double-logarithmic constraints. This result thus furnishes an infinite number of experimental data for testing the veracity of the recently proposed spectral equations for planar AdS/CFT correspondence.Comment: 43 pages; v2: references added, minor changes in the tex

Four loop twist two, BFKL, wrapping and strings

The anomalous dimensions of twist two operators have to satisfy certain consistency requirements derived from BFKL. For N=4 SYM it was shown that at four loops, the anomalous dimensions derived from the all-loop asymptotic Bethe ansatz do not pass this test. In this paper we obtain the remaining wrapping part of these anomalous dimensions from string theory and show that these contributions exactly cure the problem and lead to agreement with both LO and NLO BFKL expectations.Comment: 34 pages, 1 figure; v3: typos fixed, references added; v4: references adde

Finite size giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3

We use the algebraic curve and Luscher's mu-term to calculate the leading order finite size corrections to the dispersion relation of giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3. We consider a single magnon as well as one magnon in each SU(2). In addition the algebraic curve computation is generalized to give the leading order correction for an arbitrary multi-magnon state in the SU(2) x SU(2) sector.Comment: 19 pages; v2, v3: references added, typos fixe

Mobilność ołowiu w warunkach kwaśnych gleb Podlasia

The researches were conducted in three districts of Podlasie Region. The rcsearch coyered the determination of total content of lead and its two fractions: l (lead in soil solution, exchangeable) and l (lead bound with oxides and hydroxtdes of Fe and Mn). There was determined also pH of soils, the content of organic carbon in them, base exchange capaciry and hydrolytic acidity. It was found that the content of carbon in analyzed soils was Iow and typical for slightly contaminated soils. The content of both mobile fractions of lead was also Iow, but the percentage in total content was high and ranged between 12.8 and 36 %.Przeprowadzono badania gleb w trzech gminach Podlasia. W glebach oznaczono ogólną zawartość ołowiu i dwie jego frakcje I (ołów w roztworze glebowym oraz wymienny) i II (ołów związany z tlenkami oraz wodorotlenkami Fe i Mn). Oznaczono także pil gleb, zawartość w nich węgla organicznego, sumę zasad wymiennych i kwasowość hydrolityczną. Stwierdzono, że zawartość ołowiu w badanych glebach była bardzo mała, typowa dla gleb lekkich niezanieczyszczonych. Również zawartość obu mobilnych frakcji ołowiu była mała, ale ich udział w zawartości ogólnej był znaczny i wahał się od 12,8 do 36 %

Zawartość i skład frakcyjny niklu w glebach uprawnych zależnie od ich właściwości fizykochemicznych

The aim of this study was estimation of pseudo-total nickel content and its fractional composition in arable soils depending on their physicochemical properties.The research material consisted of samples taken from arable soil in 81 points of Podlasie Province. The content of pseudo-total nickel in soils and its fractional composition was determined with BCR method. The correlations between pseudo-total content of nickel, as well as its individual fractions and physicochemical properties of soils were evaluated. It was found, that pseudo-total content of nickel was typical for uncontaminated soils and ranged from 2.0 to 14.4 mg kg–1. The share of acid soluble and exchangeable fraction was above 20 %, as compared to pseudo-total content. Reducible fraction comprised 20–40 %. The most of nickel was bound to organic matter. The factors which influenced fractional composition of nickel were determined. For the light soils it was content of soil fraction –1. Udział frakcji wymiennej w ogólnej zawartości niklu w badanych glebach wynosił ponad 20 %. Frakcja redukowalna stanowiła 20–40 % zawartości ogólnej. Najwięcej niklu było związane z substancją organiczną. Wyodrębniono czynniki wpływające na udział niklu w poszczególnych frakcjach. Dla gleb lekkich był to skład granulometryczny, zawartość frakcji spławialnej i pH, a w przypadku gleb średnich zawartość węgla organicznego, skład granulometryczny, zawartość frakcji spławialnej i zawartość magnezu. Nie wyznaczono czynników warunkujących zawartość niklu w II i IV frakcji gleb lekkich, a w przypadku gleb średnich zawartość tego metalu we frakcji I

Light conditions effect on bird cherry ermine moth - the main pest of bird cherry

This article studies the effect of light and high temperature on various parameters describing the growth and development of bird cherry ermine moth (Yponomeuta evonymellus L.) – the main pest of bird cherry (Prunus padus L.). We found that light significantly influences the moth masses and dynamics of their development. Moths developed from larvae feeding on leaves growing in full light conditions have a higher mass and shorter time of adult eclosion from pupa in comparison with larvae feeding on leaves growing in shade. However, extremely high summer temperature significantly disturbs pupation process in Y. evonymellus population. Our laboratory experiments indicate that a critical temperature is 36°C. Above this threshold the percentage of pupation drastically decreases (from ca. 70% to 35%). The conditions of intensive sun are better for some parameters of growth and development of bird cherry ermine moth. On the other hand, extreme summer temperatures, related with global warming, may restrict the occurrence of Y. evonymellus gradation

Zawartość cynku w roślinach w zależności od jego składu frakcyjnego w glebie oraz właściwości gleby

Metals in soils occur in different forms, which are more or less mobile, which means bioavailable. The aim of this study was to assess the content of zinc in cultivated plants, depending on soil properties but also its content in soil and fractions in typical and unpolluted region, which is the Podlasie Province. The research material consisted of samples taken from arable soil in 81 points of Podlasie Province. Basic physicochemical properties and content of soil fraction frakcja związana z tlenkami i wodorotlenkami > frakcja wymienialna > frakcja rezydualna. Wśród analizowanych roślin uprawianych na glebach lekkich najwięcej cynku zawierało żyto. Rośliny uprawiane na glebach średnich, z wyjątkiem kukurydzy, zawierały zbliżone ilości cynku. Nie stwierdzono istotnych zależności pomiędzy zawartością cynku w roślinach a właściwościami gleb. Istotne zależności wystąpiły tylko w przypadku współczynnika bioakumulacji