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

TL;DR

This paper presents a novel method to construct the complete six-loop integrand for maximal super-Yang-Mills theory, overcoming computational challenges with new graph-based unitarity cut techniques applicable to various quantum field theories.

Contribution

Introduces two innovative graph-based approaches for evaluating multi-loop unitarity cuts in D dimensions, avoiding explicit state sums and sewing, applicable to a broad class of theories.

Findings

Constructed the complete six-loop four-point amplitude integrand in super-Yang-Mills.

Developed recursive and direct methods for unitarity cuts that do not rely on explicit state sums.

Methods are expected to be applicable to QCD and Einstein gravity.

Abstract

We construct the complete (planar and non-planar) integrand for the six-loop four-point amplitude in maximal $D\le10$ 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.