On a four-loop form factor in N=4

TL;DR

This paper discusses progress in computing a four-loop supersymmetric form factor in N=4 super Yang-Mills theory, involving advanced techniques like color-kinematic duality and integration-by-parts identities.

Contribution

It presents a detailed analysis of the four-loop form factor, including the application of IBP identities and rational IBP relations, advancing computational methods in supersymmetric gauge theories.

Findings

Successful reduction of the four-loop integrand using IBP identities

Introduction of rational IBP relations as a new computational tool

Cross-checks confirming the consistency of the computed form factor

Abstract

We report on progress toward computing a four-loop supersymmetric form factor in maximally supersymmetric Yang-Mills theory. A representative example particle content from the involved supermultiplets is a stress-tensor operator with two on-shell gluons. In previous work, the integrand for this form factor was obtained using color-kinematic duality in a particularly simple form. Here the result of applying integration-by-parts identities is discussed and cross-checks of the result is performed. Rational IBP relations and their reduction are introduced as a potentially useful aide.