Bootstrapping a Five-Loop Amplitude Using Steinmann Relations

TL;DR

This paper leverages Steinmann relations to significantly simplify the bootstrap process, enabling the complete determination of the five-loop six-particle amplitude in planar N=4 SYM theory.

Contribution

It introduces a novel application of Steinmann relations to streamline the amplitude bootstrap at five loops in a highly symmetric gauge theory.

Findings

Complete five-loop six-particle amplitude obtained

Steinmann relations reduce function space complexity

Enhanced understanding of amplitude analytic structure

Abstract

The analytic structure of scattering amplitudes is restricted by Steinmann relations, which enforce the vanishing of certain discontinuities of discontinuities. We show that these relations dramatically simplify the function space for the hexagon function bootstrap in planar maximally supersymmetric Yang-Mills theory. Armed with this simplification, along with the constraints of dual conformal symmetry and Regge exponentiation, we obtain the complete five-loop six-particle amplitude.