Related papers: Amplitudes at Weak Coupling as Polytopes in AdS_5

We obtain concise analytic formulae for Wilson loops computed on special n-point polygonal contours through two-loops in weakly coupled N=4 supersymmetric gauge theory. The contours we consider can be embedded into a (1+1)-dimensional…

Wilson loops with lightlike polygonal contours have been conjectured to be equivalent to MHV scattering amplitudes in N=4 super Yang-Mills. We compute such Wilson loops for special polygonal contours at two loops in perturbation theory.…

Alday & Maldacena conjectured an equivalence between string amplitudes in AdS$_5 \times S^5$ and null polygonal Wilson loops in planar $\mathcal{N}=4$ super-Yang-Mills (SYM). At strong coupling this identifies SYM amplitudes with areas of…

In this note we continue the exploration of the polytope picture for scattering amplitudes, where amplitudes are associated with the volumes of polytopes in generalized momentum-twistor spaces. After a quick warm-up example illustrating the…

In the planar N = 4 supersymmetric Yang-Mills theory at weak coupling, we perform the first analytic computation of a two-loop eight-edged Wilson loop embedded into the boundary of AdS3. Its remainder function is given as a function of…

We present compact formulas for the box coefficients of the six-point NMHV one-loop amplitudes in N=8 supergravity. We explicitly demonstrate that the corresponding box integral functions, with these coefficients, have the complete IR…

Motivated by the cluster structure of two-loop scattering amplitudes in N=4 Yang-Mills theory we define "cluster polylogarithm functions". We find that all such functions of weight 4 are made up of a single simple building block associated…

We obtain a compact expression for the octagon MHV amplitude / Wilson loop at 3 loops in planar N=4 SYM and in special 2d kinematics in terms of 7 unfixed coefficients. We do this by making use of the cyclic and parity symmetry of the…

Next-to-MHV one-loop amplitudes in N=4 gauge theory can be written as a linear combination of known multivalued functions, called scalar box functions, with coefficients that are rational functions. We consider the localization of these…

We examine the coefficients of the box functions in N=1 supersymmetric one-loop amplitudes. We present the box coefficients for all six point N=1 amplitudes and certain all $n$ example coefficients. We find for ``next-to MHV'' amplitudes…

In hep-th/9805025, a result for the symmetric 3-loop massive tetrahedron in 3 dimensions was found, using the lattice algorithm PSLQ. Here we give a more general formula, involving 3 distinct masses. A proof is devised, though it cannot be…

We define a volume function on configurations of four points in the 3-sphere which is invariant under the action of PU(2,1), the automorphism group of the CR structure defined on the sphere by its embedding in complex 2-space. We show that…

We study the correlation function of two circular Wilson loops at strong coupling in N=4 super Yang-Mills theory. Using the AdS/CFT correspondence, the problem maps to finding the minimal surface between two circles defined on the boundary…

The S-matrix for planar N = 4 super Yang-Mills theory can be computed as the correlation function for a holomorphic polygonal Wilson loop in twistor space. In an axial gauge, this leads to the construction of the all-loop integrand via MHV…

This article reviews the recent progress in twistor approaches to Wilson loops, amplitudes and their duality for N=4 super Yang-Mills. Wilson loops and amplitudes are derived from first principles using the twistor action for maximally…

We consider the two-loop four-point amplitude in N=2 super QED, and show that there exists an approximate recursive structure similar to that captured by the ABDK/BDS ansatz for MHV amplitudes in N=4 super Yang-Mills. Furthermore, we…

We compute for the first time the two-loop corrections to arbitrary n-gon lightlike Wilson loops in N=4 supersymmetric Yang-Mills theory, using efficient numerical methods. The calculation is motivated by the remarkable agreement between…

We present full analytic results for the four-point one-loop amplitude of a conformally coupled scalar in four-dimensional Anti-de-Sitter space dual to a primary operator with scaling dimension 1. The computation is based on an intriguing…

Describing the geometry of the dual amplituhedron without reference to a particular triangulation is an open problem. In this note we introduce a new way of determining the volume of the tree-level NMHV dual amplituhedron. We show that…

All-loop planar scattering amplitudes in maximally supersymmetric Yang-Mills theory can be formulated geometrically in terms of the "amplituhedron". We study the mathematical structures of the one-loop amplituhedron, and present a new…