The double spacelike collinear limit of planar N=4 SYM is governed by a generalized splitting amplitude that equals the six-point BDS-subtracted amplitude in multi-Regge kinematics.
The Three-loop MHV Octagon from $\bar{Q}$ equations
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abstract
The $\bar{Q}$ equations, rooted in the dual superconformal anomalies, are a powerful tool for computing amplitudes in planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory. By using the $\bar{Q}$ 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.
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Double spacelike collinear limits from multi-Regge kinematics
The double spacelike collinear limit of planar N=4 SYM is governed by a generalized splitting amplitude that equals the six-point BDS-subtracted amplitude in multi-Regge kinematics.