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

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.