The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory

TL;DR

This paper constructs the complete five-loop four-point amplitude of N=4 super-Yang-Mills theory, including nonplanar parts, and analyzes its ultraviolet divergence, advancing understanding of supergravity ultraviolet behavior.

Contribution

It provides the first complete D-dimensional integrand of the five-loop amplitude, including nonplanar contributions, using the method of maximal cuts.

Findings

Explicit expression for the ultraviolet divergence in critical dimension

Complete integrand including nonplanar contributions

Progress towards N=8 supergravity amplitude analysis

Abstract

Using the method of maximal cuts, we construct the complete D-dimensional integrand of the five-loop four-point amplitude of N = 4 super-Yang-Mills theory, including nonplanar contributions. In the critical dimension where this amplitude becomes ultraviolet divergent, we present a compact explicit expression for the nonvanishing ultraviolet divergence in terms of three vacuum integrals. This construction provides a crucial step towards obtaining the corresponding amplitude of N = 8 supergravity useful for resolving the general ultraviolet behavior of supergravity theories.