Bootstrapping a stress-tensor form factor through eight loops

We bootstrap the three-point form factor of the chiral stress-tensor multiplet in planar 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 gg -> Hg and H -> 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.

Automated summary

In this paper, we compute the three-point form factor of the chiral stress-tensor multiplet in planar N = 4 supersymmetric Yang-Mills theory at six, seven, and eight loops. We bootstrap the computation using boundary data from the form factor operator product expansion. By observing and employing new restrictions on pairs and triples of adjacent letters in the symbol, we obtain detailed information about the function space required to describe the form factor through eight loops. The numerical results provide strong evidence for a finite radius of convergence of perturbation theory. Our results are expected to give the highest weight part of the gg -> Hg and H -> ggg amplitudes in the heavy-top limit of QCD through eight loops. They also contribute to the recent discovery of a new antipodal duality between this form factor and a six-point amplitude in the same theory.