Related papers: Prescriptive Unitarity from Positive Geometries

Pure Yang-Mills amplitudes with all external gluons carrying positive helicity, known as all-plus amplitudes, have an especially simple structure. The tree amplitudes vanish and, up to at least two loops, the loop-level amplitudes are…

We develop a manifestly supersymmetric version of the generalized unitarity cut method for calculating scattering amplitudes in N=4 SYM theory. We illustrate the power of this method by computing the one-loop n-point NMHV super-amplitudes.…

The complete tree-level S-matrix of four dimensional ${\cal N}=4$ super Yang-Mills and ${\cal N} = 8$ supergravity has compact forms as integrals over the moduli space of certain rational maps. In this note we derive formulas for amplitudes…

Subtraction schemes provide a systematic way to compute fully-differential cross sections beyond the leading order in the strong coupling constant. These methods make singular real-emission corrections integrable in phase space by the…

We derive a systematic procedure for obtaining an explicit, L-loop leading singularities of planar N=4 super Yang-Mills scattering amplitudes in twistor space directly from their momentum space channel diagrams. The expressions are given as…

For two massless particles i and j, the collinear limit is a special kinematic configuration in which the particles propagate with parallel four-momentum vectors, with the total momentum P distributed as p_i=xP and p_j=(1-x)P, so that…

We propose a geometrical approach to generate symbol letters of amplitudes/integrals in planar $\mathcal{N}=4$ Super Yang-Mills theory, known as {\it Schubert problems}. Beginning with one-loop integrals, we find that intersections of lines…

We compute the two-loop result for the null pentagonal Wilson loop with a Lagrangian insertion (normalized by the Wilson loop without insertion) in planar, maximally supersymmetric Yang-Mills theory. This finite observable is closely…

Using the pure spinor formalism in part I [1] we compute the complete tree-level amplitude of N massless open strings and find a striking simple and compact form in terms of minimal building blocks: the full N-point amplitude is expressed…

We describe a systematic approach to the construction of loop-integrand bases at arbitrary loop-order, sufficient for the representation of general quantum field theories. We provide a graph-theoretic definition of `power-counting' for…

We introduce a novel construction of a contour deformation within the framework of Loop-Tree Duality for the numerical computation of loop integrals featuring threshold singularities in momentum space. The functional form of our contour…

In this paper we describe algebraic and diagrammatic methods, related to the MHV generating function method, for evaluating and exposing the structure of supersymmetric sums over the states crossing generalized unitarity cuts of multi-loop…

We propose multiloop vacuum amplitudes as the optimal building blocks for efficiently assembling theoretical predictions at high-energy colliders. This hypothesis is strongly supported by the manifestly causal properties of the loop-tree…

We find a permutation relation among Yangian Invariants -- two Yangian Invariants with adjacent external lines exchanged are related by a simple kinematic factor. This relation is shown to be equivalent to U(1) decoupling and…

Using loop-tree duality, we relate a renormalised $n$-point $l$-loop amplitude in a quantum field theory to a phase-space integral of a regularised $l$-fold forward limit of a UV-subtracted $(n+2l)$-point tree-amplitude-like object. We show…

We derive novel recursion relations for all loop amplitude integrands of planar, maximally supersymmetric Yang-Mills theory in terms of unitarity-like `cuts' obtained via sequences of BCFW deformations in momentum-twistor space.

Building on the seminal work of Arkani-Hamed, He, Salvatori and Thomas (AHST), we explore the positive geometry encoding one loop scattering amplitude for quartic scalar interactions. We define a new class of combinatorial polytopes that we…

We present a complete computation of superstring scattering amplitudes at tree level, for the case of Neveu-Schwarz insertions. Mathematically, this is to say that we determine explicitly the superstring measure on the moduli space…

There is evidence that one can compute tree level super Yang-Mills amplitudes using either connected or completely disconnected curves in twistor space. We argue that the two computations are equivalent, if the integration contours are…

The amplituhedron was recently introduced in the study of scattering amplitudes in $N=4$ super Yang-Mills. We compute the cohomology class of a tree amplituhedron subvariety of the Grassmannian to be the truncation of an affine Stanley…