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We construct the complete (planar and non-planar) integrand for the six-loopfour-point amplitude in maximal $D\le10$ super-Yang-Mills. This constructionemploys new advances that combat the proliferation of diagram contributions andstate sums when evaluating multi-loop $D$-dimensional unitarity cuts.Concretely, we introduce two graph-based approaches to evaluating generalizedunitarity cuts in $D$ dimensions: 1) recursively from lower-loop cuts, or 2)directly from known higher-loop planar cuts. Neither method relies on explicitstate sums or any sewing of tree-level amplitudes. These methods are based onidentities that we expect to hold for a broad family of theories, including QCDand Einstein gravity.

Maximal Super-Yang-Mills at Six Loops via Novel Integrand Bootstrap