The Steinman Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
Georgios Papathanasiou (DESY)

Scattering amplitudes form a bridge connecting theoretical particle physics with the real world of collider experiments, yet their computation by means of Feynman diagrams quickly becomes prohibitive. Focusing on the simplest case of N=4 super Yang–Mills theory, in this talk I present recent progress in bypassing these limitations and directly constructing amplitudes, by exploiting their expected analytic structure. First, I describe the discovery of new, possibly universal analytic properties known as the extended Steinmann relations, or equivalently cluster adjacency, as well as the coaction principle. Then, I demonstrate their power in computing the six-particle amplitude up to seven loops, as well as the seven-particle amplitude up to four loops, and discuss further applications.