Related papers: Positive Geometries for One-Loop Chiral Octagons

In this note, we use the new bottom up method based on soft theorems to construct the expansion of single-trace Yang-Mills-scalar amplitudes recursively. The resulted expansion manifests the gauge invariance for any polarization carried by…

Seven-point amplitudes in planar ${\cal N}=4$ super-Yang-Mills theory have previously been constructed through four loops using the Steinmann cluster bootstrap, but only at the level of the symbol. We promote these symbols to actual…

We show how studying leading singularities of Feynman diagrams, when all momenta are complex, gives a simple way of writing multi-loop and multi-particle scattering amplitudes in N=4 super Yang-Mills. The simplicity of the method is…

Infrared divergences in scattering amplitudes arise when a loop momentum $\ell$ becomes collinear with a massless external momentum $p$. In gauge theories, it is known that the L-loop logarithm of a planar amplitude has much softer infrared…

In this letter, we consider a positive geometry conjectured to encode the loop integrand of four-point stress-energy correlators in planar $\mathcal{N}=4$ super Yang-Mills. Beginning with four lines in twistor space, we characterize a…

We present an ansatz for the planar five-loop four-point amplitude in maximally supersymmetric Yang-Mills theory in terms of loop integrals. This ansatz exploits the recently observed correspondence between integrals with simple conformal…

We review current efficient techniques for the construction of multi-leg and multi-loop on-shell scattering amplitudes in supersymmetric gauge theories. Examples in the maximally supersymmetric Yang-Mills theory in four dimensions are…

We review an algorithm for determining the branch points of general amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills theory from amplituhedra. We demonstrate how to use the recent reformulation of amplituhedra in terms of `sign flips'…

N=4 supersymmetric Yang-Mills theory exhibits a rather surprising duality of Wilson-loop vacuum expectation values and scattering amplitudes. In this paper, we investigate this correspondence at the diagram level. We find that one-loop…

We propose an all-loop expression for scattering amplitudes in planar N=4 super Yang-Mills theory in multi-Regge kinematics valid for all multiplicities, all helicity configurations and arbitrary logarithmic accuracy. Our expression is…

We study correlators of null, $n$-sided polygonal Wilson loops with a Lagrangian insertion in the planar limit of the ${\cal N}=4$ supersymmetric Yang-Mills theory. This finite observable is closely related to loop integrands of…

We propose a novel type of duality that connects a sequence of well-known theories with even-multiplicity scalar amplitudes: it relates the Yang-Mills theory coupled to a specific scalar matter sector to the nonlinear sigma model on a…

We use momentum twistors to evaluate planar loop integrals. Infrared divergences are regulated by the recently proposed AdS-inspired mass regulator. We show that two-loop amplitudes in N=4 super Yang-Mills can be expanded in terms of basis…

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…

We consider the complete set of planar two-loop five-point Feynman integrals with two off-shell external legs. These integrals are relevant, for instance, for the calculation of the second-order QCD corrections to the production of two…

This article reviews recent progress in formulating double-copy constructions for scattering amplitudes in supergravity theories with N=2 supersymmetry in five and four spacetime dimensions. Particular attention is devoted to infinite…

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…

We construct the states and symmetries of N = 4 super-Yang-Mills by tensoring two N = 1 chiral multiplets and introducing two extra SUSY generators. This allows us to write the maximal N = 8 supergravity as four copies of the chiral…

We present analytic results for all planar two-loop Feynman integrals contributing to five-particle scattering amplitudes with one external massive leg. We express the integrals in terms of a basis of algebraically-independent…

Tree-level scattering amplitudes in planar N=4 super Yang-Mills are known to be Yangian-invariant. It has been shown that integrability allows to obtain a general, explicit method to find such invariants. The uplifting of this result to the…