Bootstrapping a Stress-Tensor Form Factor through 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 $gg\to Hg$ and $H\to ggg$ 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.

arXiv comment44 pages, 8 figures, 8 tables; v2, minor corrections, journal version, references added

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• Bootstrapping $\mathcal{N}=4$ sYM correlators using integrability
• Symbology for elliptic multiple polylogarithms and the symbol prime
• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• Bootstrapping elliptic Feynman integrals using Schubert analysis
• The Color-Dual Fates of $F^3$, $R^3$, and $\mathcal{N}=4$ Supergravity
• An Infinite Family of Elliptic Ladder Integrals
• Non-planar BCFW Grassmannian Geometries
• Deciphering the Maximal Transcendentality Principle via Bootstrap
• New relations for tree-level form factors and scattering amplitudes
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons