Higher point MHV amplitudes in N=4 Supersymmetric Yang-Mills Theory

TL;DR

This paper calculates specific two-loop seven-point MHV amplitudes in N=4 SYM, revealing their structure in terms of conformal integrals and introducing a new leg addition rule for amplitude coefficients.

Contribution

It provides the first detailed computation of the even part of two-loop seven-point MHV amplitudes and introduces a novel leg addition rule relating amplitudes with different numbers of points.

Findings

The even part of the amplitude is expressed via conformal integrals with simple coefficients.

No higher polygon loops appear in the computed cuts.

A leg addition rule relates n+1-point to n-point amplitude coefficients.

Abstract

We compute the even part of the two-loop seven-point planar MHV amplitude in N=4 supersymmetric Yang-Mills theory. We find that the even part is expressed in terms of conformal integrals with simple rational coefficients. We also compute the even part of two all-n cuts. An important feature of the result is that no hexagon (or higher polygon) loops appear among the integrals detected by the cuts we computed. We also present a "leg addition rule," which allows us to express some integral coefficients in the n+1-point MHV amplitude in terms of the integral coefficients of the n-point MHV amplitude.