Related papers: Logarithmic Singularities and Maximally Supersymme…
Dual conformal symmetry has had a huge impact on our understanding of planar scattering amplitudes in N=4 super Yang-Mills. At tree level, it combines with the original conformal symmetry generators to a Yangian algebra, a hallmark of…
We explore scattering amplitudes on the Coulomb branch of maximally supersymmetric Yang-Mills theory. We introduce a particular pattern of scalar vacuum expectation values that allow us to define amplitudes with a different mass pattern…
We consider four-point correlation functions of protected single-trace scalar operators in planar N = 4 supersymmetric Yang-Mills (SYM). We conjecture that all loop corrections derive from an integrand which enjoys a ten-dimensional…
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 present a method to compute the integrands of one-loop Einstein-Yang-Mills amplitudes for any number of external gauge and gravity multiplets. Our construction relies on the double-copy structure of Einstein-Yang-Mills as…
We further exploit the relation between tropical Grassmannians and $\operatorname{Gr}(4,n)$ cluster algebras in order to make and refine predictions for the singularities of scattering amplitudes in $\mathcal{N}=4$ planar super Yang-Mills…
We describe a family of finite, four-dimensional, $L$-loop Feynman integrals that involve weight-$(L+1)$ hyperlogarithms integrated over $(L-1)$-dimensional elliptically fibered varieties we conjecture to be Calabi-Yau. At three loops, we…
We study on-shell diagrams for gravity theories with any number of supersymmetries and find a compact Grassmannian formula in terms of edge variables of the graphs. Unlike in gauge theory where the analogous form involves only…
Superspace power-counting rules give estimates for the loop order at which divergences can first appear in non-renormalisable supersymmetric field theories. In some cases these estimates can be improved if harmonic superspace, rather than…
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…
We compute the even part of the two-loop seven-point planar MHV amplitude in N=4 supersymmetric Yang-Mills theory. We find that the even part is expressed in terms of conformal integrals with simple rational coefficients. We also compute…
In this paper we discuss the geometric integrand expansion of the five-point Wilson loop with one Lagrangian insertion in maximally supersymmetric Yang-Mills theory. We construct the integrand corresponding to an all-loop class of…
We revisit the familiar construction of one-loop scattering amplitudes via generalized unitarity in light of the recently understood properties of loop integrands prior to their integration. We show how in any four-dimensional quantum field…
We develop an iterative method for constructing four-dimensional generalized unitarity cuts in $\mathcal{N} = 2$ supersymmetric Yang-Mills (SYM) theory coupled to fundamental matter hypermultiplets ($\mathcal{N} = 2$ SQCD). For iterated…
We present an all-orders formula for the six-point amplitude of planar maximally supersymmetric N=4 Yang-Mills theory in the leading-logarithmic approximation of multi-Regge kinematics. In the MHV helicity configuration, our results agree…
Scattering amplitudes in planar ${\cal N}=4$ supersymmetric Yang-Mills theory are dual to expectation values of null polygonal Wilson loops. The Amplituhedron provides a geometric construction for the all-loop integrand as the canonical…
Integrands for colour ordered scattering amplitudes in planar N=4 SYM are dual to those of correlation functions of the energy-momentum multiplet of the theory. The construction can relate amplitudes with different numbers of legs. By graph…
We demonstrate that the tree-level amplitudes of maximal super-Yang-Mills theory in six dimensions, when stripped of their overall momentum and supermomentum delta functions, are covariant with respect to the six-dimensional dual conformal…
We study a novel geometric expansion for scattering amplitudes in the planar sector of N=4 super Yang-Mills theory, in the context of the Amplituhedron which reproduces the all-loop integrand as a canonical differential form on the positive…
We review various aspects of cluster algebras and the ways in which they appear in the study of loop-level amplitudes in planar ${\cal N} = 4$ supersymmetric Yang-Mills theory. In particular, we highlight the different forms of…