A Cluster Bootstrap for Two-Loop MHV Amplitudes

Understand

We apply a bootstrap procedure to two-loop MHV amplitudes in planar N=4 super-Yang-Mills theory.

• We argue that the mathematically most complicated part (the $\Lambda^2 B_2$ coproduct component) of the n-particle amplitude is uniquely determined by a simple cluster algebra property together with a few physical constraints (dihedral symmetry, analytic structure, supersymmetry, and well-defined collinear limits).
• We present a concise, closed-form expression which manifests these properties for all n.