On the Factorisation of the Connected Prescription for Yang-Mills Amplitudes

We examine factorisation in the connected prescription of Yang-Mills amplitudes. The multi-particle pole is interpreted as coming from representing delta functions as meromorphic functions. However, a naive evaluation does not give a correct result. We give a simple prescription for the integration contour which does give the correct result. We verify this prescription for a family of gauge-fixing conditions.Comment: 16 pages, 1 figur

Defect multiplets of N=1 supersymmetry in 4d

Any 4d theory possessing $\mathcal{N}=1$ supersymmetry admits a so called $\mathcal{S}$-multiplet, containing the conserved energy-momentum tensor and supercurrent. When a defect is introduced into such a theory, the $\mathcal{S}$-multiplet receives contributions localised on the defect, which indicate the breaking of some translation symmetry and consequently also some supersymmetries. We call this the defect multiplet. We classify such terms corresponding to half-BPS defects which can be either three-dimensional, preserving 3d $\mathcal{N}=1$, or two-dimensional, preserving $\mathcal{N}=(0,2)$. The new terms localised on the defect furnish multiplets of the reduced symmetry and give rise to the displacement operator

Cutkosky representation and direct integration

We present a new method of direct integration of Feynman integrals based on the Cutkosky representation of the integrals. In this representation we are able to explicitly compute the integrals which yield square root singularities and leave only the integrals which yield logarithmic singularities, thus making the transcendentality weight manifest. The method is elementary, algorithmic, does not introduce spurious non-physical singularities and does not require a reduction to a basis of pure integrals

Classical Polylogarithms for Amplitudes and Wilson Loops

We present a compact analytic formula for the two-loop six-particle MHV remainder function (equivalently, the two-loop light-like hexagon Wilson loop) in N = 4 supersymmetric Yang-Mills theory in terms of the classical polylogarithm functions Li_k with cross-ratios of momentum twistor invariants as their arguments. In deriving our result we rely on results from the theory of motives.Comment: 11 pages, v2: journal version, minor corrections and simplifications, additional details available at http://goo.gl/Cl0

A Grassmannian Etude in NMHV Minors

Arkani-Hamed, Cachazo, Cheung and Kaplan have proposed a Grassmannian formulation for the S-matrix of N=4 Yang-Mills as an integral over link variables. In parallel work, the connected prescription for computing tree amplitudes in Witten's twistor string theory has also been written in terms of link variables. In this paper we extend the six- and seven-point results of arXiv:0909.0229 and arXiv:0909.0499 by providing a simple analytic proof of the equivalence between the two formulas for all tree-level NMHV superamplitudes. Also we note that a simple deformation of the connected prescription integrand gives directly the ACCK Grassmannian integrand in the limit when the deformation parameters equal zero.Comment: 17 page

Factorized Tree-level Scattering in AdS_4 x CP^3

AdS_4/CFT_3 duality relating IIA string theory on AdS_4 x CP^3 to N=6 superconformal Chern-Simons theory provides an arena for studying aspects of integrability in a new potentially exactly solvable system. In this paper we explore the tree-level worldsheet scattering for strings on AdS_4 x CP^3. We compute all bosonic four-, five- and six-point amplitudes in the gauge-fixed action and demonstrate the absence of particle production.Comment: 23 pages, v2. references adde