The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory

TL;DR

This paper analytically computes the differential of two-loop MHV amplitudes in N=4 super Yang-Mills theory, revealing a deep connection with cluster algebra structures and expressing results solely in terms of polylogarithm functions.

Contribution

It provides the first explicit analytic form of the differential of two-loop MHV amplitudes using polylogarithms and highlights the role of cluster X-coordinates in the amplitude structure.

Findings

Amplitudes expressed in terms of Li_k(-x) functions for k=1,2,3

Arguments x are dual conformal cross-ratios from cluster X-coordinates

Demonstrates the cluster structure underlies amplitude properties

Abstract

We present an explicit analytic calculation of the differential of the planar n-particle, two-loop MHV scattering amplitude in N=4 super Yang-Mills theory. The result is expressed only in terms of the polylogarithm functions Li_k(-x), for k=1,2,3, with arguments x belonging to the special class of dual conformal cross-ratios known as cluster X-coordinates. The surprising fact that these amplitudes may be expressed in this way provides a striking example of the manner in which the cluster structure on the kinematic configuration space underlies the structure of amplitudes in SYM theory.