Talks

I review how N=4 SYM can be reformulated as a theory on twistor space, and explain various calculations that have been performed there. In particular, twistors turn out to be a powerful tool for investigating the duality between scattering amplitudes and null polygonal Wilson Loops in the planar limit. The BCFW recursion relations are interpreted as the loop equations for a supersymmetric generalization of the Wilson Loop.

The S-matrix of N=4 super Yang-Mills in the planar limit enjoys a remarkable duality with non-BPS null polygon Wilson loops in the same theory, but with the role of momenta and position interchanged. I will attempt to explain how such a duality works, by stressing how familiar notions such as factorization limits, unitarity and the loop integrand translate into simple and verifiable statements about Wilson loops. This requires a suitable supersymmetric extension of Wilson loops, which I will describe. I will then discuss recent progress in using the full supersymmetry of the theory on the Wilson loop side to simplify scattering amplitude computations

We study the four-point correlation function of stress-tensor supermultiplets in N=4 SYM using the method of Lagrangian insertions. We argue that, as a corollary of N=4 superconformal symmetry, the resulting all-loop integrand possesses an unexpected complete symmetry under the exchange of the four external and all the internal (integration) points. This alone allows us to predict the integrand of the three-loop correlation function up to four undetermined constants. Further, exploiting the conjectured amplitude/correlation function duality, we are able to fully determine the three-loop integrand in the planar limit. We perform an independent check of this result by verifying that it is consistent with the operator product expansion, in particular that it correctly reproduces the three-loop anomalous dimension of the Konishi operator. As a byproduct of our study, we also obtain the three-point function of two half-BPS operators and one Konishi operator at three-loop level. We use the same technique to work out a compact form for the four-loop four-point integrand and discuss the generalisation to higher loops.

I will give a brief review on the subject of scattering amplitudes in N=4 super Yang-Mills focussing on their infinite dimensional symmetry structure at tree-level and the fate of these symmetries at loop-level in particular employing a Highs-Regulator for the IR divergencies.