We present the complete integrands of five-point superamplitudes in $\mathcal{N}=4$ super-Yang-Mills theory and $\mathcal{N}=8$ supergravity, at one and two loops, for four-dimensional external states and $D$-dimensional internal kinematics. For $\mathcal{N}=4$ super-Yang-Mills theory we give the amplitudes for general gauge group—including all nonplanar contributions. The results are constructed using integral diagrams that manifestly satisfy the conjectured duality between color and kinematics, providing additional nontrivial evidence in favor of the duality for multipoint and multiloop amplitudes. We determine the ultraviolet poles by integrating the amplitudes in the dimensions where logarithmic divergences first occur. We introduce new kinematic prefactors which offer a convenient decomposition of the external state structure of the nonplanar five-point amplitudes in the maximally supersymmetric theories to all loop orders.

• Received 4 July 2011

DOI:https://doi.org/10.1103/PhysRevD.85.025006