The Two-Loop Remainder Function for Eight and Nine Particles

Understand

Two-loop MHV amplitudes in planar ${\cal N} = 4$ supersymmetric Yang Mills theory are known to exhibit many intriguing forms of cluster-algebraic structure.

• We leverage this structure to upgrade the symbols of the eight- and nine-particle amplitudes to complete analytic functions.
• This is done by systematically projecting onto the components of these amplitudes that take different functional forms, and matching each component to an ansatz of multiple polylogarithms with negative cluster-coordinate arguments.
• The remaining additive constant can be determined analytically by comparing the collinear limit of each amplitude to known lower-multiplicity results.