Related papers: Prescriptive Unitarity from Positive Geometries
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…
We find that unitarity cuts and the duality between color and kinematics are sufficient constraints to bootstrap $D$-dimensional QCD scattering amplitudes starting from three-particle tree-level. Specifically, we calculate tree level…
This note addresses the problem of spurious poles in gauge-theoretic scattering amplitudes. New twistor coordinates for the momenta are introduced, based on the concept of dual conformal invariance. The cancellation of spurious poles for a…
We use the infrared consistency of one-loop amplitudes in N=4 Yang-Mills theory to derive a compact analytic formula for a tree-level NNMHV gluon scattering amplitude in QCD, the first such formula known. We argue that the IR conditions,…
We provide a new set of on-shell recursion relations for tree-level scattering amplitudes, which are valid for any non-trivial theory of massless particles. In particular, we reconstruct the scattering amplitudes from (a subset of) their…
Scattering amplitudes in planar N=4 super Yang-Mills theory reveal a remarkable symmetry structure. In addition to the superconformal symmetry of the Lagrangian of the theory, the planar amplitudes exhibit a dual superconformal symmetry.…
The hypersimplex $\Delta_{k+1,n}$ is the image of the positive Grassmannian $Gr^{\geq 0}_{k+1,n}$ under the moment map. It is a polytope of dimension $n-1$ in $\mathbb{R}^n$. Meanwhile, the amplituhedron $\mathcal{A}_{n,k,2}(Z)$ is the…
A main conjecture in the field of Positive Geometry states that amplituhedra, which are certain semi-algebraic sets in the Grassmannian, are positive geometries. It is motivated by examples showing that the canonical forms of certain…
Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary…
The leading order $N$-point energy correlators of maximally supersymmetric Yang-Mills theory in the limit where the $N$ detectors are collinear can be expressed as an integral of the $1\to N$ splitting function, which is given by the…
Supersymmetric integrands for the two-loop five-point amplitudes in ten-dimensional super Yang--Mills and type II supergravity are proposed. The kinematic numerators are manifestly local and satisfy the duality between color and kinematics…
The geometry of the dual amplituhedron is generally described in reference to a particular triangulation. A given triangulation manifests only certain aspects of the underlying space while obscuring others, therefore understanding this…
In this note we make a field-theoretical derivation of a series of new recursion relations by a one-parameter deformation of kinematic variables for tree and one-loop amplitudes of bi-adjoint $\phi^3$ theory. Tree amplitudes are given by…
We derive an on-shell diagram recursion for tree-level scattering amplitudes in $\mathcal{N}=7$ supergravity. The diagrams are evaluated in terms of Grassmannian integrals and momentum twistors, generalising previous results of Hodges in…
In this sequel to arXiv:1711.11507 we classify the boundaries of amplituhedra relevant for determining the branch points of general two-loop amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills theory. We explain the connection to on-shell…
The construction of amplitudes on curved space-times is a major challenge, particularly when the background has non-constant curvature. We give formulae for all tree-level graviton scattering amplitudes in curved self-dual radiative…
We construct all supergravity theories that can be obtained through factorized orbifold projections of N=8 supergravity, exposing their double-copy structure, and calculate their one-loop four-point scattering amplitudes. We observe a…
The (tree) amplituhedron A(n,k,m) is the image in the Grassmannian Gr(k,k+m) of the totally nonnegative part of Gr(k,n), under a (map induced by a) linear map which is totally positive. It was introduced by Arkani-Hamed and Trnka in 2013 in…
The collinear factorization properties of two-loop scattering amplitudes in dimensionally-regulated N=4 super-Yang-Mills theory suggest that, in the planar ('t Hooft) limit, higher-loop contributions can be expressed entirely in terms of…
We present an algorithm for writing down explicit formulas for all tree amplitudes in N=8 supergravity, obtained from solving the supersymmetric on-shell recursion relations. The formula is patterned after one recently obtained for all tree…