A Cluster Bootstrap for Two-Loop MHV Amplitudes

Abstract

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.

v2: a few comments added

References in corpus (5)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• An Operator Product Expansion for Polygonal null Wilson Loops
• Bootstrapping an NMHV amplitude through three loops
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM