All tree-level amplitudes in N=4 SYM

We give an explicit formula for all tree amplitudes in N=4 SYM, derived by solving the recently presented supersymmetric tree-level recursion relations. The result is given in a compact, manifestly supersymmetric form and we show how to extract from it all possible component amplitudes for an arbitrary number of external particles and any arrangement of external particles and helicities. We focus particularly on extracting gluon amplitudes which are valid for any gauge theory. The formula for all tree-level amplitudes is given in terms of nested sums of dual superconformal invariants and it therefore manifestly respects both conventional and dual superconformal symmetry.Comment: 26 pages. Boundary terms in sums corrected. Additional references. Acknowledgement added. Extended discussion. One new figur

The DiSC assay - A cost-effective guide to treatment for chronic lymphocytic leukemia?

The differential staining cytotoxicity (DISC) assay involves in vitro drug panel testing against patient tumor cells to identify optimal therapy. This observational study investigated whether DISC assay guided treatment could improve outcome in patients with chronic lymphocytic leukemia. A cohort of 178 patients were categorized either as sensitive to drugs in vitro and receiving a sensitive drug in vivo, sensitive in vitro but not treated with a sensitive drug, or having disease resistant to all drugs tested in vitro. Response and survival for these patient categories were compared using multivariate regression techniques. Patients receiving a sensitive drug, compared with those who though having sensitivity did not, had a higher remission rate (odds ratio, 6.5; 95% CI, 2.91-14.53) and reduced death rate (hazard ratio, 0.29; 95% CI, 0.16-0.53). Having adjusted for all known confounding factors, the results suggest that in vitro drug sensitivity is an important independent prognostic variable to include in future trials, and that the DiSC assay may be a cost-effective use of health resources: the estimated incremental cost-effectiveness was $1,470 per life-year gained. A randomized controlled trial is required to confirm the benefit and estimate reliably the potential impact of assay-guided choice of therapy

Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory

Tree-level scattering amplitudes in N=4 super Yang-Mills theory have recently been shown to transform covariantly with respect to a 'dual' superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra psu(2,2|4) of the theory. In this paper we derive the action of the dual superconformal generators in on-shell superspace and extend the dual generators suitably to leave scattering amplitudes invariant. We then study the algebra of standard and dual symmetry generators and show that the inclusion of the dual superconformal generators lifts the psu(2,2|4) symmetry algebra to a Yangian. The non-local Yangian generators acting on amplitudes turn out to be cyclically invariant due to special properties of psu(2,2|4). The representation of the Yangian generators takes the same form as in the case of local operators, suggesting that the Yangian symmetry is an intrinsic property of planar N=4 super Yang-Mills, at least at tree level.Comment: 23 pages, no figures; v2: typos corrected, references added; v3: minor changes, references adde

The UK NHS Economic Evaluation Database : Economic issues in evaluations of health technology

Objective: The U.K. NHS Economic Evaluation Database (EED) project is commissioned to identify papers on economic evaluations of health technologies and to disseminate their findings to NHS decision makers by means of structured abstracts that are available through a public database and the Cochrane Library. This paper discusses current issues relating to the economic aspects of producing NHS EED abstracts. Methods: A review of NHS EED was undertaken between 1994 and 1999 to determine the methodologies adopted and issues that influence the usefulness of economic evaluations. Methods adopted to improve the quality of NHS EED abstracts are also reported. Results: Eighty-five percent of NHS EED abstracts are cost-effectiveness analyses (CEAs), 9.3% are cost-utility analyses (CUAs), and only 1.4% are cost-benefit analyses (CBAs). Of the total abstracts, 65.9% are based on single studies, 19.5% on reviews, 3.9% on estimates of effectiveness, and 10.7% on combinations of these sources. Models are utilized in 16.7% of CEAs, 60.2% of CUAs, and 20% of CBAs. Analyses of CBA studies reveal a degree of misuse of well-established definitions. NHS EED internal control mechanisms are reported that provide a means of ensuring that abstracts are based on sound academic principles. Conclusions: Most economic evaluations are conducted by means of CEA, followed by CUA, while CBA accounts for an extreme minority of cases. Single studies form the principal source of effectiveness data, although models are widely used, principally in CUA. The structure of NHS EED abstracts provides decision makers with the principal results and an interpretation of the relative strengths and weaknesses of economic evaluations

Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory

We prove the MHV vertex expansion for all tree amplitudes of N=4 SYM theory. The proof uses a shift acting on all external momenta, and we show that every N^kMHV tree amplitude falls off as 1/z^k, or faster, for large z under this shift. The MHV vertex expansion allows us to derive compact and efficient generating functions for all N^kMHV tree amplitudes of the theory. We also derive an improved form of the anti-NMHV generating function. The proof leads to a curious set of sum rules for the diagrams of the MHV vertex expansion.Comment: 40 pages, 7 figure

Kappa-symmetric deformations of M5-brane dynamics

We calculate the first supersymmetric and kappa-symmetric derivative deformation of the M5-brane worldvolume theory in a flat eleven-dimensional background. By applying cohomological techniques we obtain a deformation of the standard constraint of the superembedding formalism. The first possible deformation of the constraint and hence the equations of motion arises at cubic order in fields and fourth order in a fundamental length scale $l$. The deformation is unique up to this order. In particular this rules out any induced Einstein-Hilbert terms on the worldvolume. We explicitly calculate corrections to the equations of motion for the tensor gauge supermultiplet.Comment: 17 pages. Additional comments in section

Kappa-symmetric Derivative Corrections to D-brane Dynamics

We show how the superembedding formalism can be applied to construct manifestly kappa-symmetric higher derivative corrections for the D9-brane. We also show that all correction terms appear at even powers of the fundamental length scale $l$. We explicitly construct the first potential correction, which corresponds to the kappa-symmetric version of the $\partial^4 F^4$, which one finds from the four-point amplitude of the open superstring.Comment: 20 pages. Minor changes, added reference

Null Wilson loops with a self-crossing and the Wilson loop/amplitude conjecture

The present study illuminates the relation between null cusped Wilson loops and their corresponding amplitudes. We find that, compared to the case with no self-crossing, the one loop expectation value of a self-intersecting Wilson loop develops an additional 1/\epsilon singularity associated to the intersection. Interestingly, the same 1/\epsilon pole exists in the finite part of the one loop amplitude, appearing in the BDS conjecture, at the corresponding kinematic limit. At two loops, we explore the behaviour of the remainder function R, encoding the deviation of the amplitude from the BDS conjecture. By analysing the renormalisation group equations for the Wilson loop with a simple self-crossing, we argue that, when approaching the configuration with a self-crossing (u_2 \to 1, u_1\approx u_3), R diverges in the imaginary direction like R ~ i \pi \log^3(1-u_2). This behaviour can be attributed to the non-trivial analytic continuation needed when passing from the Euclidean to the physical region and suggests that R has a branch cut in the negative u_2 axis when the two other cross ratios are approximately equal (u_1 \approx u_3).Comment: 23 pages, 1 figure, typos corrected,references adde

On the covariance of the Dirac-Born-Infeld-Myers action

A covariant version of the non-abelian Dirac-Born-Infeld-Myers action is presented. The non-abelian degrees of freedom are incorporated by adjoining to the (bosonic) worldvolume of the brane a number of anticommuting fermionic directions corresponding to boundary fermions in the string picture. The proposed action treats these variables as classical but can be given a matrix interpretation if a suitable quantisation prescription is adopted. After gauge-fixing and quantisation of the fermions, the action is shown to be in agreement with the Myers action derived from T-duality. It is also shown that the requirement of covariance in the above sense leads to a modified WZ term which also agrees with the one proposed by Myers.Comment: 18 pages. Minor alterations to the text; references adde

A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon

Seven-particle scattering amplitudes in planar super-Yang-Mills theory are believed to belong to a special class of generalised polylogarithm functions called heptagon functions. These are functions with physical branch cuts whose symbols may be written in terms of the 42 cluster A-coordinates on Gr(4, 7). Motivated by the success of the hexagon bootstrap programme for constructing six-particle amplitudes we initiate the systematic study of the symbols of heptagon functions. We find that there is exactly one such symbol of weight six which satisfies the MHV last-entry condition and is finite in the 7 ? 6 collinear limit. This unique symbol is both dihedral and parity-symmetric, and remarkably its collinear limit is exactly the symbol of the three-loop six-particle MHV amplitude, although none of these properties were assumed a priori. It must therefore be the symbol of the threeloop seven-particle MHV amplitude. The simplicity of its construction suggests that the n-gon bootstrap may be surprisingly powerful for n > 6