Flux-tube methods for scattering amplitudes in planar N=4 SYM theory

In this talk, I will explain how to compute gluon scattering amplitudes in planar N=4 Super-Yang-Mills theory using the flux tube (OPE) picture. The latter, which builds on the duality with light-like Wilson loops, provides essentially a description of the scattering amplitudes in terms of excitations evolving on a two-dimensional background. Exploiting the remarkable integrable structures of this background, one can formulate and investigate this way scattering amplitudes, at any values of the ‘t Hooft coupling, as an expansion around the multi-collinear (a.k.a. OPE) limit. I shall report on recent progress made in this direction and speculate on its possible application to the study of scattering amplitudes in the multi-Regge kinematics.