Higher point maximally helicity violating amplitudes inN=4supersymmetric Yang-Mills theory

Abstract

We compute the even part of the two-loop seven-point planar MHV amplitude in $\mathcal{N}=4$ 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.