Proof of a three-loop relation between the Regge limits of four-point amplitudes in N=4 SYM and N=8 supergravity

TL;DR

This paper establishes a three-loop relation between the Regge limits of four-point amplitudes in N=4 SYM and N=8 supergravity, simplifying the expressions to ladder diagrams and supporting a potential exact relation.

Contribution

It proves a three-loop relation between the Regge limits of four-point amplitudes in N=4 SYM and N=8 supergravity, confirming previous all-loop conjectures.

Findings

Regge limits simplify to sums over ladder diagrams

Results are consistent with the eikonal representation

Supports the possibility of an exact three-loop amplitude relation

Abstract

A previously proposed all-loop-orders relation between the Regge limits of four-point amplitudes of N=4 supersymmetric Yang-Mills theory and N=8 supergravity is established at the three-loop level. We show that the Regge limit of known expressions for the amplitudes obtained using generalized unitarity simplifies in both cases to a (modified) sum over three-loop ladder and crossed-ladder scalar diagrams. This in turn is consistent with the result obtained using the eikonal representation of the four-point gravity amplitude. A possible exact three-loop relation between four-point amplitudes is also considered.