A cluster bootstrap for two-loop MHV amplitudes

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 B-2(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.