The planar two-loop four-point form factor in maximally supersymmetric Yang-Mills theory

TL;DR

This paper derives the two-loop four-point form factor integrand in planar $ ext{N}=4$ super-Yang-Mills theory using a special basis, enabling direct evaluation and comparison with bootstrap results, and paving the way for exploring dualities.

Contribution

It introduces a novel integrand basis with triangle powercounting for two-loop form factors in $ ext{N}=4$ SYM, facilitating direct computation and validation of existing bootstrap results.

Findings

Derived the four-dimensional integrand for the four-particle form factor at two loops.

Utilized a basis with unit leading singularities on all residues.

Set the stage for independent confirmation and exploration of dualities in $ ext{N}=4$ SYM.

Abstract

We derive the four-dimensional integrand of the maximal-helicity-violating four-particle form factor for the chiral part of the stress-tensor supermultiplet in planar $\mathcal{N}=4$ super-Yang-Mills theory at two loops. In our integrand construction, we adopt a special integrand basis with triangle powercounting where each basis element has unit leading singularities on all co-dimension eight residues. This basis was first constructed in the context of two-loop $n$-point scattering amplitudes in $\mathcal{N}=4$ beyond the planar limit and we describe here, how to directly utilize it for the form factor computation. Our result sets the stage for an independent confirmation of the symbol level bootstrap results of Dixon et al.~via direct evaluation. The imminent availability of all relevant two-loop five-point, one-mass master integrals will permit further investigations of a set of marvelous (self-)dualities between form factors and scattering amplitudes in planar $\mathcal{N}=4$ in the near future.