Related papers: Some analytic results for two-loop scattering ampl…
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…
In this paper we consider multi-loop integrals appearing in MHV scattering amplitudes of planar N=4 SYM. Through particular differential operators which reduce the loop order by one, we present explicit equations for the two-loop…
We present an explicit analytic calculation of the differential of the planar n-particle, two-loop MHV scattering amplitude in N=4 super Yang-Mills theory. The result is expressed only in terms of the polylogarithm functions Li_k(-x), for…
We propose a first implementation of the integrand-reduction method for two-loop scattering amplitudes. We show that the residues of the amplitudes on multi-particle cuts are polynomials in the irreducible scalar products involving the loop…
This thesis is focused on the development of new mathematical methods for computing multi-loop scattering amplitudes in gauge theories. In this work we combine, for the first time, the unitarity-based construction for integrands, and the…
We describe a general algorithm which builds on several pieces of data available in the literature to construct explicit analytic formulas for two-loop MHV amplitudes in N=4 super-Yang-Mills theory. The non-classical part of an amplitude is…
Using the duality between color and kinematics, we construct two-loop four-point scattering amplitudes in $\mathcal{N}=2$ super-Yang-Mills (SYM) theory coupled to $N_f$ fundamental hypermultiplets. Our results are valid in $D\le 6$…
We derive analytic results for the symbol of certain two-loop Feynman integrals relevant for seven- and eight-point two-loop scattering amplitudes in planar $\mathcal{N}=4$ super-Yang--Mills theory. We use a bootstrap inspired strategy,…
We propose a new diagrammatic formulation of the all-loop scattering amplitudes/Wilson loops in planar N=4 SYM, dubbed the "momentum-twistor diagrams". These are on-shell-diagrams obtained by gluing trivalent black and white vertices…
We use the relation of the one-loop subleading-color amplitudes to the one-loop $n$-point leading color amplitudes in ${\cal N}=4$ SYM, to derive a polytope interpretation for the former in the $MHV$ case, and a representation in momentum…
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 describe the application of a novel approach for the reduction of scattering amplitudes, based on multivariate polynomial division, which we have recently presented. This technique yields the complete integrand decomposition for…
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 highlight the latest developments in computing higher-order scattering amplitudes with massive internal propagators. The contributing Feynman integrals often lead to special classes of functions, for example, functions associated with…
We give an explicit recursive formula for the all L-loop integrand for scattering amplitudes in N=4 SYM in the planar limit, manifesting the full Yangian symmetry of the theory. This generalizes the BCFW recursion relation for tree…
Two-loop MHV amplitudes in planar ${\cal N} = 4$ supersymmetric Yang Mills theory are known to exhibit many intriguing forms of cluster-algebraic structure. We leverage this structure to upgrade the symbols of the eight- and nine-particle…
Recently, an explicit, recursive formula for the all-loop integrand of planar scattering amplitudes in N=4 SYM has been described, generalizing the BCFW formula for tree amplitudes, and making manifest the Yangian symmetry of the theory.…
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 compute the simplest one-loop planar amplitudes in Higgsed ABJM theory at a generic point of the moduli space. We explicitly check that they can be expressed in terms of integrals which are invariant under dual conformal symmetry…
We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity…