Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity

TL;DR

This paper computes complete five-point superamplitudes in N=4 super-Yang-Mills and N=8 supergravity at one and two loops, providing evidence for color-kinematics duality and analyzing ultraviolet divergences.

Contribution

It presents the full integrands for five-point amplitudes including non-planar contributions, and introduces new kinematic factors for better decomposition of external states.

Findings

Amplitudes constructed for general gauge groups including non-planar parts.

Evidence supporting the color-kinematics duality at multipoint and multiloop levels.

Identification of ultraviolet poles in specific dimensions.

Abstract

We present the complete integrands of five-point superamplitudes in N=4 super-Yang-Mills theory and N=8 supergravity, at one and two loops, for four-dimensional external states and D-dimensional internal kinematics. For N=4 super-Yang-Mills theory we give the amplitudes for general gauge group -- including all non-planar 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.