Two-Loop Iteration of Five-PointN=4Super-Yang-Mills Amplitudes

We confirm by explicit computation the conjectured all-orders iteration of planar maximally supersymmetric $\mathcal{N}=4$ Yang-Mills theory in the nontrivial case of five-point two-loop amplitudes. We compute the required unitarity cuts of the integrand and evaluate the resulting integrals numerically using a Mellin-Barnes representation and the automated package of Czakon [ Comput. Phys. Commun. 175, 559 (2006)]. This confirmation of the iteration relation provides further evidence suggesting that $\mathcal{N}=4$ gauge theory is solvable.