Iterative Structure Within The Five-Particle Two-Loop Amplitude

TL;DR

This paper uncovers an unexpected iterative pattern in the two-loop five-gluon amplitude in N=4 supersymmetric Yang-Mills theory, linking complex two-loop integrals to simpler one-loop diagrams, which could influence understanding of amplitude structures.

Contribution

It reveals a novel iterative relation within the two-loop five-gluon amplitude, connecting complex integrals to one-loop scalar box diagrams in N=4 SYM.

Findings

A subset of two-loop diagrams satisfies an iterative relation.

The relation involves a two-loop pentagon-box integral and one-loop scalar box diagrams.

Implications for the structure of the full two-loop amplitude are discussed.

Abstract

We find an unexpected iterative structure within the two-loop five-gluon amplitude in N = 4 supersymmetric Yang-Mills theory. Specifically, we show that a subset of diagrams contributing to the full amplitude, including a two-loop pentagon-box integral with nontrivial dependence on five kinematical variables, satisfies an iterative relation in terms of one-loop scalar box diagrams. The implications of this result for the possible iterative structure of the full two-loop amplitude are discussed.