The Three-loop MHV Octagon from $\bar{Q}$ equations

Abstract

The Q equations, rooted in the dual superconformal anomalies, are a powerful tool for computing amplitudes in planar N = 4 supersymmetric Yang-Mills theory. By using the Q equations, we compute the symbol of the first MHV amplitude with algebraic letters -the three-loop 8-point amplitude (or the octagon remainder function) -in this theory. The symbol alphabet for this amplitude consists of 204 independent rational letters and shares the same 18 algebraic letters with the two-loop 8-point NMHV amplitude.