Bootstrapping a Stress-Tensor Form Factor through Eight Loops

TL;DR

This paper computes the three-point form factor of the stress-tensor multiplet in planar $ abla=4$ SYM theory up to eight loops, providing insights into perturbative convergence and connections to QCD amplitudes.

Contribution

It presents the highest perturbative order calculation of a multi-variate quantity in a four-dimensional quantum field theory, using bootstrap methods and boundary data from the operator product expansion.

Findings

Evidence for a finite radius of convergence of perturbation theory.

New restrictions on symbol letters in the form factor.

Results suggest highest weight parts of certain QCD amplitudes at eight loops.

Abstract

We bootstrap the three-point form factor of the chiral stress-tensor multiplet in planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory at six, seven, and eight loops, using boundary data from the form factor operator product expansion. This may represent the highest perturbative order to which multi-variate quantities in a unitary four-dimensional quantum field theory have been computed. In computing this form factor, we observe and employ new restrictions on pairs and triples of adjacent letters in the symbol. We provide details about the function space required to describe the form factor through eight loops. Plotting the results on various lines provides striking numerical evidence for a finite radius of convergence of perturbation theory. By the principle of maximal transcendentality, our results are expected to give the highest weight part of the $g g \rightarrow H g$ and $H \rightarrow ggg$ amplitudes in the heavy-top limit of QCD through eight loops. These results were also recently used to discover a new antipodal duality between this form factor and a six-point amplitude in the same theory.