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 $\mathcal{N}=4$ 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.

36 pages, 4 figures, 5 tables, 1 ancillary file. Contribution to the proceedings of the Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2019), 31 August - 25 September 2019, Corfu, Greece

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