From correlation functions to Wilson loops

We start with an n-point correlation function in a conformal gauge theory. We show that a special limit produces a polygonal Wilson loop with $n$ sides. The limit takes the $n$ points towards the vertices of a null polygonal Wilson loop such that successive distances $x^2_{i,i+1} \to 0$. This produces a fast moving particle that generates a "frame" for the Wilson loop. We explain in detail how the limit is approached, including some subtle effects from the propagation of a fast moving particle in the full interacting theory. We perform perturbative checks by doing explicit computations in N=4 super-Yang-Mills.Comment: 37 pages, 10 figures; typos corrected, references adde

From Correlators to Wilson Loops in Chern-Simons Matter Theories

We study n-point correlation functions for chiral primary operators in three dimensional supersymmetric Chern-Simons matter theories. Our analysis is carried on in N=2 superspace and covers N=2,3 supersymmetric CFT's, the N=6 ABJM and the N=8 BLG models. In the limit where the positions of adjacent operators become light-like, we find that the one-loop n-point correlator divided by its tree level expression coincides with a light-like n-polygon Wilson loop. Remarkably, the result can be simply expressed as a linear combination of five dimensional two-mass easy boxes. We manage to evaluate the integrals analytically and find a vanishing result, in agreement with previous findings for Wilson loops.Comment: 32 pages, 6 figures, JHEP

On form factors in N=4 sym

In this paper we study the form factors for the half-BPS operators $\mathcal{O}^{(n)}_I$ and the $\mathcal{N}=4$ stress tensor supermultiplet current $W^{AB}$ up to the second order of perturbation theory and for the Konishi operator $\mathcal{K}$ at first order of perturbation theory in $\mathcal{N}=4$ SYM theory at weak coupling. For all the objects we observe the exponentiation of the IR divergences with two anomalous dimensions: the cusp anomalous dimension and the collinear anomalous dimension. For the IR finite parts we obtain a similar situation as for the gluon scattering amplitudes, namely, apart from the case of $W^{AB}$ and $\mathcal{K}$ the finite part has some remainder function which we calculate up to the second order. It involves the generalized Goncharov polylogarithms of several variables. All the answers are expressed through the integrals related to the dual conformal invariant ones which might be a signal of integrable structure standing behind the form factors.Comment: 35 pages, 7 figures, LATEX2

Fermionic T-duality in the pp-wave limit

AdS5 X S5 and its pp-wave limit are self-dual under transformations involving eight fermionic T-dualities, a property which accounts for symmetries seen in scattering amplitudes in N=4 super-Yang-Mills. Despite strong evidence for similar symmetries in the amplitudes of three-dimensional N=6 ABJM theory, a corresponding self-duality in the dual geometry AdS4 X CP3 currently eludes us. Here, working with the type IIA pp-wave limit of AdS4 X CP3 preserving twenty four supercharges, we show that the pp-wave is self-dual with respect to eight commuting fermionic T-dualities and not the six expected. In addition, we show the same symmetry can be found in a superposition pp-wave and a generic pp-wave with twenty and sixteen unbroken supersymmetries respectively, strongly suggesting that self-duality under fermionic T-duality may be a symmetry of all pp-waves.Comment: 21 pages, typos fixe

Bounds for the global cyclicity index of a general network via weighted majorization

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Oestradiol-17β plasma concentrations after intramuscular injection of oestradiol benzoate or oestradiol cypionate in llamas (Lama glama)

<p>Abstract</p> <p>Background</p> <p>Llamas (<it>Lama glama</it>) are induced ovulators and the process of ovulation depends on dominant follicular size. In addition, a close relationship between behavioural estrus and ovulation is not registered in llamas. Therefore, the exogenous control of follicular development with hormones aims to predict the optimal time to mate. Oestradiol-17β (E₂) and its esters are currently used in domestic species, including camelids, in synchronization treatments. But, in llamas, there is no reports regarding the appropriate dosages to be used and most protocols have been designed by extrapolation from those recommended for other ruminants. The aim of the present study was to characterize plasma E₂concentrations in intact female llamas following a single intramuscular (i.m.) injection of two oestradiol esters: oestradiol benzoate (EB) and oestradiol cypionate (ECP).</p> <p>Methods</p> <p>Twelve non pregnant and non lactating sexually mature llamas were i.m. injected on day 0 with 2.5 mg of EB (EB group, n = 6) or ECP (ECP group, n = 6). Blood samples were collected immediately before injection, at 1, 6, 12, 24 h after treatment and then daily until day 14 post injection. Changes in hormone concentrations with time were analyzed in each group by analysis of variance (ANOVA) using a repeated measures (within-SS) design. Plasma E₂concentrations and area under the concentration-time curve (AUC) values were compared between groups by ANOVA. In all cases a Least-Significant Difference test (LSD) was used to determine differences between means. Hormonal and AUC data are expressed as mean ± S.E.M.</p> <p>Results</p> <p>Peak plasma E₂concentrations were achieved earlier and were higher in EB group than in ECP group. Thereafter, E₂returned to physiological concentrations earlier in EB group (day 5) than in ECP group (day 9). Although plasma E₂profiles differed over time among groups there were no differences between them on AUC values.</p> <p>Conclusions</p> <p>The i.m. injection of a single dose of both oestradiol esters resulted in plasma E₂concentrations exceeding physiological values for a variable period. Moreover, the plasma E₂profiles observed depended on the derivative of oestradiol administered. This basic information becomes relevant at defining treatment protocols including oestrogens in llamas.</p

Solution to the Ward Identities for Superamplitudes

Supersymmetry and R-symmetry Ward identities relate on-shell amplitudes in a supersymmetric field theory. We solve these Ward identities for (Next-to)^K MHV amplitudes of the maximally supersymmetric N=4 and N=8 theories. The resulting superamplitude is written in a new, manifestly supersymmetric and R-invariant form: it is expressed as a sum of very simple SUSY and SU(N)_R-invariant Grassmann polynomials, each multiplied by a "basis amplitude". For (Next-to)^K MHV n-point superamplitudes the number of basis amplitudes is equal to the dimension of the irreducible representation of SU(n-4) corresponding to the rectangular Young diagram with N columns and K rows. The linearly independent amplitudes in this algebraic basis may still be functionally related by permutation of momenta. We show how cyclic and reflection symmetries can be used to obtain a smaller functional basis of color-ordered single-trace amplitudes in N=4 gauge theory. We also analyze the more significant reduction that occurs in N=8 supergravity because gravity amplitudes are not ordered. All results are valid at both tree and loop level.Comment: 29 pages, published versio

Scattering Amplitudes/Wilson Loop Duality In ABJM Theory

For N=6 superconformal Chern-Simons-matter theories in three dimensions, by a direct superspace Feynman diagram approach, we compute the two-loop four-point scattering amplitude with external chiral matter fields. We find that the result is in perfect agreement with the two-loop result for a light-like four-polygon Wilson loop. This is a nontrivial evidence of the scattering amplitudes/Wilson loop duality in three dimensions. Moreover, both the IR divergent and the finite parts of our two-loop result agree with a BDS-like ansatz for all-loop amplitudes where the scaling function is given in terms of the N=4 SYM one, according to the conjectured Bethe equations for ABJM. Consequently, we are able to make a prediction for the four-loop correction to the amplitude. We also discuss the dual conformal invariance of the two-loop result.Comment: 1+16 pages, 2 figures, minor modifications and references adde