Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality
Jacob L. Bourjaily, Paul Heslop, Vuong-Viet Tran
TL;DR
This work extends the eight-loop perturbative data for the four-point amplitude and the four-point stress-tensor correlator in planar ${N}=4$ SYM using the soft-collinear bootstrap and the amplitude–correlator duality. It uncovers two key novelties at eight loops: strictly finite conformal integrals and pseudoconformal integrals that diverge off-shell, indicating a breakdown of manifest conformality term-by-term while preserving full dual-conformal symmetry in the integrand. Coefficients of all contributing dual-conformal integrands are fixed by the vanishing residue of the logarithm of the amplitude in the soft-collinear limit, with the correlator side providing essential input to resolve finite terms; the authors present a complete eight-loop amplitude and correlator consistent with these constraints. The results reveal new coefficient structures, the appearance of divergences tied to higher-loop subgraphs, and elliptic-cut phenomena, highlighting a deeper tension between locality, planarity, and conformality in ${N}=4$ SYM and offering a rich dataset for further exploration of perturbative structure.
Abstract
We use the soft-collinear bootstrap to construct the 8-loop integrand for the 4-point amplitude and 4-stress-tensor correlation function in planar maximally supersymmetric Yang-Mills theory. Both have a unique representation in terms of planar, conformal integrands grouped according to a hidden symmetry discovered for correlation functions. The answer we find exposes a fundamental tension between manifest locality and planarity with manifest conformality not seen at lower loops. For the first time, the integrand must include terms that are finite even on-shell and terms that are divergent even off-shell (so-called `pseudoconformal' integrals). We describe these novelties and their consequences in this letter, and we make the full correlator and amplitude available as part of this work's submission files to the arXiv.