Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops

TL;DR

This paper develops a systematic approach to compute five-loop four-point amplitudes in maximally supersymmetric Yang-Mills theory, leveraging conformal properties and unitarity cuts, aiding in testing the AdS/CFT correspondence.

Contribution

It introduces a new ansatz for five-loop amplitudes using conformal integral properties and generalized unitarity, advancing the calculation of higher-loop amplitudes in supersymmetric gauge theories.

Findings

Identified all relevant integrals with conformal properties for five-loop amplitudes.

Determined amplitude coefficients using generalized unitarity and maximal cuts.

Facilitated future calculations of the cusp anomalous dimension and amplitude resummation.

Abstract

We present an ansatz for the planar five-loop four-point amplitude in maximally supersymmetric Yang-Mills theory in terms of loop integrals. This ansatz exploits the recently observed correspondence between integrals with simple conformal properties and those found in the four-point amplitudes of the theory through four loops. We explain how to identify all such integrals systematically. We make use of generalized unitarity in both four and D dimensions to determine the coefficients of each of these integrals in the amplitude. Maximal cuts, in which we cut all propagators of a given integral, are an especially effective means for determining these coefficients. The set of integrals and coefficients determined here will be useful for computing the five-loop cusp anomalous dimension of the theory which is of interest for non-trivial checks of the AdS/CFT duality conjecture. It will also be useful for checking a conjecture that the amplitudes have an iterative structure allowing for their all-loop resummation, whose link to a recent string-side computation by Alday and Maldacena opens a new venue for quantitative AdS/CFT comparisons.