The steinmann cluster bootstrap for N = 4 super yang-mills amplitudes

Abstract

We review the bootstrap method for constructing six- and seven-particle amplitudes in planar N = 4 super Yang-Mills theory, by exploiting their analytic structure. We focus on two recently discovered properties which greatly simplify this construction at symbol and function level, respectively: The extended Steinmann relations, or equivalently cluster adjacency, and the coaction principle. We then demonstrate their power in determining the six-particle amplitude through six and seven loops in the NMHV and MHV sectors respectively, as well as the symbol of the NMHV seven-particle amplitude to four loops.