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

Authors: John Joseph Carrasco,  Alexander Edison,  Henrik Johansson

Preprint number: UUITP-62/21

Abstract: We construct the complete (planar and non-planar) integrand for the six-loop four-point amplitude in maximal D=<10 super-Yang-Mills. This construction employs new advances that combat the proliferation of diagram contributions and state sums when evaluating multi-loop D-dimensional unitarity cuts.  Concretely, we introduce two graph-based approaches to evaluating generalized unitarity cuts in D dimensions: 1) recursively from lower-loop cuts, or 2) directly from known higher-loop planar cuts. Neither method relies on explicit state sums or any sewing of tree-level amplitudes.  These methods are based on identities that we expect to hold for a broad family of theories, including  QCD and Einstein gravity.