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Scattering amplitudes in Yang-Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space---fully localized on the support of the scattering equations. Because solving the…

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 introduce a machine-learning framework based on symbolic regression to extract the full symbol alphabet of multi-loop Feynman integrals. By targeting the analytic structure rather than reduction, the method is broadly applicable and…

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…

Here we construct N=4 SuperYang-Mills 6 point NMHV loop amplitude (amplitudes with three minus helicities) as a full superspace form, using the $SU(4)_{R}$ anti-commuting spinor variables. Amplitudes with different external particle and…

We construct a prescriptive, bubble power-counting basis of one-loop integrands suitable for representing amplitude integrands in less-supersymmetric Yang-Mills theory. With the exception of massless bubbles, all integrands have…

The calculation of scattering amplitudes in Yang-Mills theory at loop level is important for the analysis of background processes at particle colliders as well as our understanding of perturbation theory at the quantum level. We present…

We provide an analytic formula for the (rescaled) one-loop scalar hexagon integral $\tilde\Phi_6$ with all external legs massless, in terms of classical polylogarithms. We show that this integral is closely connected to two integrals…

We compute the non-MHV one-loop seven-gluon amplitudes in N=4 super-Yang-Mills theory, which contain three negative-helicity gluons and four positive-helicity gluons. There are four independent color-ordered amplitudes, (- - - + + + +), (-…

The planar scattering amplitudes of $\mathcal{N} = 4$ super-Yang--Mills theory display symmetries and structures which underlie their relatively simple analytic properties such as having only logarithmic singularities and no poles at…

We consider the planar MHV amplitude in N=4 supersymmetric Yang-Mills theory for 2 -> 4 particle scattering at two and three loops in the Regge kinematics. We perform an analytic continuation of two-loop result for the remainder function…

Kinematic numerators of Yang-Mills scattering amplitudes possess a rich Lie algebraic structure that suggest the existence of a hidden infinite-dimensional kinematic algebra. Explicitly realizing such a kinematic algebra is a longstanding…

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 provide evidence through two loops, that rational letters of polylogarithmic Feynman integrals are captured by the Landau equations, when the latter are recast as a polynomial of the kinematic variables of the integral, known as the…

Recent progress on scattering amplitudes has benefited from the mathematical technology of symbols for efficiently handling the types of polylogarithm functions which frequently appear in multi-loop computations. The symbol for all two-loop…

We compute the two-loop four-point MHV form factor of the stress-tensor supermultiplet in planar ${\cal N}=4$ super Yang-Mills (SYM). This form factor is analogous to the Higgs plus four-gluon amplitudes in the heavy-top limit of QCD when…

We analyze the near-collinear limit of the null polygonal hexagon super Wilson loop in the planar N = 4 superYang-Mills theory. We focus on its Grassmann components which are dual to next-to-maximal helicity-violating (NMHV) scattering…

In the planar N=4 supersymmetric Yang-Mills theory, the conformal symmetry constrains multi-loop n-edged Wilson loops to be basically given in terms of the one-loop n-edged Wilson loop, augmented, for n greater than 6, by a function of…

Scattering amplitudes in superconformal field theories do not enjoy this symmetry, because the definition of asymptotic states involve a notion of infinity. Concentrating on planar $\mathcal{N}=4$ Yang-Mills, we consider a generalization of…

We compute the symbol of the two-loop five-point amplitude in $\mathcal N=8$ supergravity. We write an ansatz for the amplitude whose rational prefactors are based on not only 4-dimensional leading singularities, but also $d$-dimensional…