Cluster adjacency and the four-loop NMHV heptagon

A bstract We exploit the recently described property of cluster adjacency for scattering amplitudes in planar N=4 N = 4 super Yang-Mills theory to construct the symbol of the four-loop NMHV heptagon amplitude. We use a manifestly cluster adjacent ansatz and describe how the parameters of this ansatz are determined using simple physical consistency requirements. We then specialise our answer for the amplitude to the multi-Regge limit, finding agreement with previously available results up to the next-to-leading logarithm, and obtaining new predictions up to (next-to) 3 -leading-logarithmic accuracy.