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We bootstrap the three-point form factor of the chiral stress-tensor multiplet in planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory at six, seven, and eight loops, using boundary data from the form factor operator product expansion.…

We propose a geometrical approach to generate symbol letters of amplitudes/integrals in planar $\mathcal{N}=4$ Super Yang-Mills theory, known as {\it Schubert problems}. Beginning with one-loop integrals, we find that intersections of lines…

We investigate the sign patterns of coefficients in the Ehrhart polynomial of the Cartesian product between the $r$-th pyramid over the Reeve tetrahedron and the hypercube $[0, n]^n$. This investigation yields partial results on the sign…

Higher-order corrections to the MSSM Higgs-boson masses are desirable for accurate predictions currently testable at the LHC. By comparing the prediction with the measured value of the discovered Higgs signal, viable parameter regions can…

Motivated by a new term-wise factorised formula for the two-loop MHV integrand for scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills (SYM), together with recent results for the five-point negative ladders in loop space, we present…

Wilson loops with lightlike polygonal contours have been conjectured to be equivalent to MHV scattering amplitudes in N=4 super Yang-Mills. We compute such Wilson loops for special polygonal contours at two loops in perturbation theory.…

We examine in detail the structure of the Regge limit of the (nonplanar) ${\cal N}=4$ SYM four-point amplitude. We begin by developing a basis of color factors $C_{ik}$ suitable for the Regge limit of the amplitude at any loop order, and…

We compute for the first time the two-loop corrections to arbitrary n-gon lightlike Wilson loops in N=4 supersymmetric Yang-Mills theory, using efficient numerical methods. The calculation is motivated by the remarkable agreement between…

Singularities hidden in the collinear region around an external massless leg may lead to conformal symmetry breaking in otherwise conformally invariant finite loop momentum integrals. For an $\ell$-loop integral, this mechanism leads to a…

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…

We discuss how to compute maximal-helicity-violating (MHV) form factors for the chiral part of the stress-tensor supermultiplet from periodic light-like polygon Wilson loops in planar $\mathcal N=4$ super Yang-Mills theory beyond the…

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 study the relationship between the momentum twistor MHV vertex expansion of planar amplitudes in N=4 super-Yang-Mills and the all-loop generalization of the BCFW recursion relations. We demonstrate explicitly in several examples that the…

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 identify cluster algebras for planar kinematics of conformal Feynman integrals in four dimensions, as sub-algebras of that for top-dimensional $G(4,n)$ corresponding to $n$-point massless kinematics. We provide evidence that they encode…

We investigate how the positive geometry framework for loop integrands in $\mathcal{N}{=}4$ super Yang-Mills theory constrains the structure of the integrated answers. This is done in the context of a geometric expansion of Wilson loops…

We discuss what predictions can be made for one-loop superamplitudes in maximally supersymmetric Yang-Mills theory by using anomalous dual conformal symmetry. We show that the anomaly coefficient is a specific combination of two-mass hard…

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 present the computation of the eight-particle three-loop amplitude beyond leading logarithmic accuracy in the multi-Regge limit of planar N=4 Super Yang-Mills theory. Starting from the all-loop dispersion integral form of the amplitude,…

Two-loop corrections to scattering amplitudes are crucial theoretical input for collider physics. Recent years have seen tremendous advances in computing Feynman integrals, scattering amplitudes, and cross sections for five-particle…