Hidden Beauty in Multiloop Amplitudes

TL;DR

This paper introduces a new differential operator method to study iteration relations in multiloop amplitudes of N=4 supersymmetric Yang-Mills theory, simplifying the analysis without full loop integral evaluations.

Contribution

It presents a novel approach using linear differential operators to analyze iteration relations, potentially proving them at all loops up to logarithmic polynomials.

Findings

Method successfully applied to two-loop amplitudes

Suggests proof of iteration relations at all loops

Simplifies analysis by avoiding full loop integral calculations

Abstract

Planar L-loop maximally helicity violating amplitudes in N = 4 supersymmetric Yang-Mills theory are believed to possess the remarkable property of satisfying iteration relations in L. We propose a simple new method for studying the iteration relations for four-particle amplitudes which involves the use of certain linear differential operators and eliminates the need to fully evaluate any loop integrals. We carry out this procedure in explicit detail for the two-loop amplitude and argue that this method can be used to prove the iteration relations to all loops up to polynomials in logarithms.