The three-loop MHV octagon from $$ \overline{Q} $$ equations
Zhenjie Li, Chi Zhang
Abstract
A bstract The $$ \overline{Q} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>Q</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> equations, rooted in the dual superconformal anomalies, are a powerful tool for computing amplitudes in planar $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 supersymmetric Yang-Mills theory. By using the $$ \overline{Q} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>Q</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> 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.