Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality

TL;DR

This paper constructs the 8-loop integrand for key quantities in planar maximally supersymmetric Yang-Mills theory, revealing new structures and a fundamental tension between locality, planarity, and conformality at high loops.

Contribution

It introduces the first 8-loop integrand for 4-point amplitudes and correlators, uncovering pseudoconformal integrals and a breakdown of manifest conformality.

Findings

Discovery of pseudoconformal integrals at eight loops

Identification of tension between locality, planarity, and conformality

Full integrand and correlator provided for further analysis

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.