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

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.