The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory

Understand

We present the complete four-loop four-point amplitude in N=4 super-Yang-Mills theory, for a general gauge group and general D-dimensional covariant kinematics, and including all non-planar contributions.

• We use the method of maximal cuts --- an efficient application of the unitarity method --- to construct the result in terms of 50 four-loop integrals.
• We give graphical rules, valid in D-dimensions, for obtaining various non-planar contributions from previously-determined terms.
• We examine the ultraviolet behavior of the amplitude near D=11/2.