Consistency Conditions on S-Matrix of Spin 1 Massless Particles

Motivated by new techniques in the computation of scattering amplitudes of massless particles in four dimensions, like BCFW recursion relations, the question of how much structure of the S-matrix can be determined from purely S-matrix arguments has received new attention. The BCFW recursion relations for massless particles of spin 1 and 2 imply that the whole tree-level S-matrix can be determined in terms of three-particle amplitudes (evaluated at complex momenta). However, the known proofs of the validity of the relations rely on the Lagrangian of the theory, either by using Feynman diagrams explicitly or by studying the effective theory at large complex momenta. This means that a purely S-matrix theoretic proof of the relations is still missing. The aim of this paper is to provide such a proof for spin 1 particles by extending the four-particle test introduced by P. Benincasa and F. Cachazo in arXiv:0705.4305[hep-th] to all particles. We show how n-particle tests imply that the rational function built from the BCFW recursion relations possesses all the correct factorization channels including holomorphic and anti-holomorphic collinear limits. This in turn implies that they give the correct S-matrix of the theory.Comment: 24 pages, 4 figure

Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops

We calculate form factors of half-BPS operators in N=4 super Yang-Mills theory at tree level and one loop using novel applications of recursion relations and unitarity. In particular, we determine the expression of the one-loop form factors with two scalars and an arbitrary number of positive-helicity gluons. These quantities resemble closely the MHV scattering amplitudes, including holomorphicity of the tree-level form factor, and the expansion in terms of two-mass easy box functions of the one-loop result. Next, we compare our result for these form factors to the calculation of a particular periodic Wilson loop at one loop, finding agreement. This suggests a novel duality relating form factors to periodic Wilson loops.Comment: 26 pages, 10 figures. v2: typos fixed, comments adde

Unraveling L_{n,k}: Grassmannian Kinematics

It was recently proposed that the leading singularities of the S-Matrix of N = 4 super Yang-Mills theory arise as the residues of a contour integral over a Grassmannian manifold, with space-time locality encoded through residue theorems generalizing Cauchy's theorem to more than one variable. We provide a method to identify the residue corresponding to any leading singularity, and we carry this out very explicitly for all leading singularities at tree level and one-loop. We also give several examples at higher loops, including all generic two-loop leading singularities and an interesting four-loop object. As a special case we consider a 12-pt N^4MHV leading singularity at two loops that has a new kinematic structure involving double square roots. Our analysis results in a simple picture for how the topological structure of loop graphs is reflected in various substructures within the Grassmannian.Comment: 26+11 page

The S-Matrix in Twistor Space

The simplicity and hidden symmetries of (Super) Yang-Mills and (Super)Gravity scattering amplitudes suggest the existence of a "weak-weak" dual formulation in which these structures are made manifest at the expense of manifest locality. We suggest that this dual description lives in (2,2) signature and is naturally formulated in twistor space. We recast the BCFW recursion relations in an on-shell form that begs to be transformed into twistor space. Our twistor transformation is inspired by Witten's, but differs in treating twistor and dual twistor variables more equally. In these variables the three and four-point amplitudes are amazingly simple; the BCFW relations are represented by diagrammatic rules that precisely define the "twistor diagrams" of Andrew Hodges. The "Hodges diagrams" for Yang-Mills theory are disks and not trees; they reveal striking connections between amplitudes and suggest a new form for them in momentum space. We also obtain a twistorial formulation of gravity. All tree amplitudes can be combined into an "S-Matrix" functional which is the natural holographic observable in asymptotically flat space; the BCFW formula turns into a quadratic equation for this "S-Matrix", providing a holographic description of N=4 SYM and N=8 Supergravity at tree level. We explore loop amplitudes in (2,2) signature and twistor space, beginning with a discussion of IR behavior. We find that the natural pole prescription renders the amplitudes well-defined and free of IR divergences. Loop amplitudes vanish for generic momenta, and in twistor space are even simpler than their tree-level counterparts! This further supports the idea that there exists a sharply defined object corresponding to the S-Matrix in (2,2) signature, computed by a dual theory naturally living in twistor space.Comment: V1: 46 pages + 23 figures. Less telegraphic abstract in the body of the paper. V2: 49 pages + 24 figures. Largely expanded set of references included. Some diagrammatic clarifications added, minor typo fixe

Note on New KLT relations

In this short note, we present two results about KLT relations discussed in recent several papers. Our first result is the re-derivation of Mason-Skinner MHV amplitude by applying the S_{n-3} permutation symmetric KLT relations directly to MHV amplitude. Our second result is the equivalence proof of the newly discovered S_{n-2} permutation symmetric KLT relations and the well-known S_{n-3} permutation symmetric KLT relations. Although both formulas have been shown to be correct by BCFW recursion relations, our result is the first direct check using the regularized definition of the new formula.Comment: 15 Pages; v2: minor correction

Generating MHV super-vertices in light-cone gauge

We constructe the $\mathcal{N}=1$ SYM lagrangian in light-cone gauge using chiral superfields instead of the standard vector superfield approach and derive the MHV lagrangian. The canonical transformations of the gauge field and gaugino fields are summarised by the transformation condition of chiral superfields. We show that $\mathcal{N}=1$ MHV super-vertices can be described by a formula similar to that of the $\mathcal{N}=4$ MHV super-amplitude. In the discussions we briefly remark on how to derive Nair's formula for $\mathcal{N}=4$ SYM theory directly from light-cone lagrangian.Comment: 25 pages, 7 figures, JHEP3 style; v2: references added, some typos corrected; Clarification on the condition used to remove one Grassmann variabl

Note on Bonus Relations for N=8 Supergravity Tree Amplitudes

We study the application of non-trivial relations between gravity tree amplitudes, the bonus relations, to all tree-level amplitudes in N=8 supergravity. We show that the relations can be used to simplify explicit formulae of supergravity tree amplitudes, by reducing the known form as a sum of (n-2)! permutations obtained by solving on-shell recursion relations, to a new form as a (n-3)!-permutation sum. We demonstrate the simplification by explicit calculations of the next-to-maximally helicity violating (NMHV) and next-to-next-to-maximally helicity violating (N^2MHV) amplitudes, and provide a general pattern of bonus coefficients for all tree-level amplitudes.Comment: 21 pages, 9 figures; v2, minor changes, references adde

The contribution of DNA ploidy to radiation sensitivity in human tumour cell lines

The contribution of DNA ploidy to radiation sensitivity was investigated in a group of eight human tumour cell lines. As previous studies suggest, while more aneuploid tumours tend to be more radioresistant, there is no significant relationship between ploidy and radiation sensitivity (SF2). The failure to observe a significant effect of ploidy on radiation sensitivity is due to the complex and multifactorial basis of radiation sensitivity. When we determined the relationship between survival and radiation-induced chromosome aberration frequency, a measure independent of most other modifiers of sensitivity, we observed a direct relationship between ploidy and mean lethal aberration frequency. The mean lethal frequency of aberrations increased from about 1 for diploid cells to about 2 for tetraploid cells. The mean lethal frequency of aberrations was independent of DNA repair variations. These observations demonstrate that changes in DNA ploidy are an important contributor to radiation sensitivity variations in human tumour cell lines. Therefore, any battery of predictive assays should include DNA ploidy measurements. © 1999 Cancer Research Campaig

Exceptional sperm cooperation in the wood mouse

Spermatozoa from a single male will compete for fertilization of ova with spermatozoa from another male when present in the female reproductive tract at the same time. Close genetic relatedness predisposes individuals towards altruism, and as haploid germ cells of an ejaculate will have genotypic similarity of 50%, it is predicted that spermatozoa may display cooperation and altruism to gain an advantage when inter-male sperm competition is intense. We report here the probable altruistic behaviour of spermatozoa in an eutherian mammal. Spermatozoa of the common wood mouse, Apodemus sylvaticus, displayed a unique morphological transformation resulting in cooperation in distinctive aggregations or 'trains' of hundreds or thousands of cells, which significantly increased sperm progressive motility. Eventual dispersal of sperm trains was associated with most of the spermatozoa undergoing a premature acrosome reaction. Cells undergoing an acrosome reaction in aggregations remote from the egg are altruistic in that they help sperm transport to the egg but compromise their own fertilizing ability

Incidence and duration of total occlusion of the radial artery in newborn infants after catheter removal

The incidence and duration of total occlusion of the radial artery after catheter removal was determined using repeated Doppler flow measurements. Thirty-two newborn infants with birthweights ranging from 945 g to 3890 g (median 1935 g) and gestational age ranging from 26 to 40 weeks (median 32 weeks) were studied. In 20 out of 32 infants (63%), complete occlusion of the radial artery occurred. The number of occlusions were not related to birthweight, gestational age or duration of cannulation. In all infants, blood flow in the radial artery resumed within 1-29 days after catheter removal. The duration of occlusion was directly related to the duration of cannulation and inversely related to birthweight. This study demonstrates a high frequency of total occlusion of the radial artery in newborn infants after percutaneous radial artery cannulation. In the majority of infants with a radial artert catheter, blood flow to the tissue distal to the cannulation site is dependent solely on the existence of an adequate arterial palmar collateral circulation