The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
Γεώργιος Παπαθανασίου, Simon Caron-Huot, Lance J. Dixon, J. M. Drummond, Falko Dulat, Jack Foster, Ömer Gürdoğan, Matt von Hippel, Andrew J. McLeod
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.