Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions

The spinor helicity formalism in four dimensions has become a very useful tool both for understanding the structure of amplitudes and also for practical numerical computation of amplitudes. Recently, there has been some discussion of an extension of this formalism to higher dimensions. We describe a particular implementation of the spinor-helicity method in ten dimensions. Using this tool, we study the tree-level S-matrix of ten dimensional super Yang-Mills theory, and prove that the theory enjoys a dual conformal symmetry. Implications for four-dimensional computations are discussed.Comment: 24 pages, 1 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

Yangian symmetry of light-like Wilson loops

We show that a certain class of light-like Wilson loops exhibits a Yangian symmetry at one loop, or equivalently, in an Abelian theory. The Wilson loops we discuss are equivalent to one-loop MHV amplitudes in N=4 super Yang-Mills theory in a certain kinematical regime. The fact that we find a Yangian symmetry constraining their functional form can be thought of as the effect of the original conformal symmetry associated to the scattering amplitudes in the N=4 theory.Comment: 15 pages, 5 figure

Massive amplitudes on the Coulomb branch of N=4 SYM

We initiate a systematic study of amplitudes with massive external particles on the Coulomb-branch of N=4 super Yang Mills theory: 1) We propose that (multi-)soft-scalar limits of massless amplitudes at the origin of moduli space can be used to determine Coulomb-branch amplitudes to leading order in the mass. This is demonstrated in numerous examples. 2) We find compact explicit expressions for several towers of tree-level amplitudes, including scattering of two massive W-bosons with any number of positive helicity gluons, valid for all values of the mass. 3) We present the general structure of superamplitudes on the Coulomb branch. For example, the n-point "MHV-band" superamplitude is proportional to a Grassmann polynomial of mixed degree 4 to 12, which is uniquely determined by supersymmetry. We find explicit tree-level superamplitudes for this MHV band and for other simple sectors of the theory. 4) Dual conformal generators are constructed, and we explore the dual conformal properties of the simplest massive amplitudes. Our compact expressions for amplitudes and superamplitudes should be of both theoretical and phenomenological interest; in particular the tree-level results carry over to truncations of the theory with less supersymmetry.Comment: 29 pages, 1 figur

Simple superamplitudes in higher dimensions

We provide simple superspaces based on a formulation of spinor helicity in general even dimensions. As a distinguishing feature these spaces admit a fermionic super-momentum conserving delta function solution to the on-shell supersymmetry Ward identities. Using these solutions, we present beautifully simple formulae for the complete three, four and five point superamplitudes in maximal super Yang-Mills theory in eight dimensions, and for the three and four point superamplitudes in ten dimensional type IIB supergravity. In addition, we discuss the exceptional kinematics of the three point amplitude, and the supersymmetric spinorial BCFW recursion, in general dimensions.Comment: 34 page

The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM

We give an explicit recursive formula for the all L-loop integrand for scattering amplitudes in N=4 SYM in the planar limit, manifesting the full Yangian symmetry of the theory. This generalizes the BCFW recursion relation for tree amplitudes to all loop orders, and extends the Grassmannian duality for leading singularities to the full amplitude. It also provides a new physical picture for the meaning of loops, associated with canonical operations for removing particles in a Yangian-invariant way. Loop amplitudes arise from the "entangled" removal of pairs of particles, and are naturally presented as an integral over lines in momentum-twistor space. As expected from manifest Yangian-invariance, the integrand is given as a sum over non-local terms, rather than the familiar decomposition in terms of local scalar integrals with rational coefficients. Knowing the integrands explicitly, it is straightforward to express them in local forms if desired; this turns out to be done most naturally using a novel basis of chiral, tensor integrals written in momentum-twistor space, each of which has unit leading singularities. As simple illustrative examples, we present a number of new multi-loop results written in local form, including the 6- and 7-point 2-loop NMHV amplitudes. Very concise expressions are presented for all 2-loop MHV amplitudes, as well as the 5-point 3-loop MHV amplitude. The structure of the loop integrand strongly suggests that the integrals yielding the physical amplitudes are "simple", and determined by IR-anomalies. We briefly comment on extending these ideas to more general planar theories.Comment: 46 pages; v2: minor changes, references adde

The Structure of n-Point One-Loop Open Superstring Amplitudes

In this article we present the worldsheet integrand for one-loop amplitudes in maximally supersymmetric superstring theory involving any number n of massless open string states. The polarization dependence is organized into the same BRST invariant kinematic combinations which also govern the leading string correction to tree level amplitudes. The dimensions of the bases for both the kinematics and the associated worldsheet integrals is found to be the unsigned Stirling number S_3^{n-1} of first kind. We explain why the same combinatorial structures govern on the one hand finite one-loop amplitudes of equal helicity states in pure Yang Mills theory and on the other hand the color tensors at quadratic alpha prime order of the color dressed tree amplitude.Comment: 75 pp, 8 figs, harvmac TeX, v2: published versio

Migratory marker expression in fibroblast foci of idiopathic pulmonary fibrosis

BACKGROUND: Fibroblast foci (FF) are considered a relevant morphologic marker of idiopathic pulmonary fibrosis/usual interstitial pneumonia (IPF/UIP), and are recognised as sites where fibrotic responses are initiated and/or perpetuated in this severe disease. Despite their relevance, the cellular and molecular mechanisms responsible for the formation of FF and their role in tissue remodelling are poorly defined. In previous studies we have provided evidence of abnormal activation of the wnt-signaling-pathway in IPF/UIP that is centred on FF and the overlying epithelium. This important morphogenetic pathway is able to trigger epithelial-mesenchymal-transition (EMT), a mechanism involved in developmental and metastatic processes, which is also potentially involved in pulmonary fibrosis. METHODS: Since EMT is characterised by enhancement of migratory potential of cells, we investigated the molecular profile of FF in 30 biopsies of IPF/UIP and a variety of control samples, focussing on the immunohistochemical expression of three molecules involved in cell motility and invasiveness, namely laminin-5-γ2-chain, fascin, and heat-shock-protein-27. RESULTS: We provide evidence that in UIP these three molecules are abnormally expressed in discrete clusters of bronchiolar basal cells precisely localised in FF. These cellular clusters expressed laminin-5-γ2-chain and heat-shock-protein-27 at very high levels, forming characteristic three-layered lesions defined as "sandwich-foci" (SW-FF). Upon quantitative analysis SW-FF were present in 28/30 UIP samples, representing more than 50% of recognisable FF in 21/30, but were exceedingly rare in a wide variety of lung pathologies examined as controls. In UIP, SW-FF were often observed in areas of microscopic honeycombing, and were also found at the interface between normal lung tissue and areas of dense scarring. CONCLUSION: These molecular abnormalities strongly suggest that SW-FF represent the leading edge of pulmonary remodelling, where abnormal migration and re-epithelialisation take place, and that abnormal proliferation and migration of bronchiolar basal cells have a major role in the remodelling process characterising IPF/UIP. Further investigations will assess their possible use as reliable markers for better defining the UIP-pattern in difficult cases

Association of childhood trauma with cognitive function in healthy adults: a pilot study

BACKGROUND: Animal and human studies suggest that stress experienced early in life has detrimental consequences on brain development, including brain regions involved in cognitive function. Cognitive changes are cardinal features of depression and posttraumatic stress disorder. Early-life trauma is a major risk factor for these disorders. Only few studies have measured the long-term consequences of childhood trauma on cognitive function in healthy adults. METHODS: In this pilot study, we investigated the relationship between childhood trauma exposure and cognitive function in 47 healthy adults, who were identified as part of a larger study from the general population in Wichita, KS. We used the Cambridge Neuropsychological Test Automated Battery (CANTAB) and the Wide-Range-Achievement-Test (WRAT-3) to examine cognitive function and individual achievement. Type and severity of childhood trauma was assessed by the Childhood Trauma Questionnaire (CTQ). Data were analyzed using multiple linear regression on CANTAB measures with primary predictors (CTQ scales) and potential confounders (age, sex, education, income). RESULTS: Specific CTQ scales were significantly associated with measures of cognitive function. Emotional abuse was associated with impaired spatial working memory performance. Physical neglect correlated with impaired spatial working memory and pattern recognition memory. Sexual abuse and physical neglect were negatively associated with WRAT-3 scores. However, the association did not reach the significance level of p < 0.01. CONCLUSIONS: Our results suggest that physical neglect and emotional abuse might be associated with memory deficits in adulthood, which in turn might pose a risk factor for the development of psychopathology