Bootstrapping six-gluon scattering in planar ${\cal N}=4$ super-Yang-Mills theory

TL;DR

This paper develops a bootstrap approach to compute six-gluon scattering amplitudes in planar ${ m N}=4$ super-Yang-Mills theory, leveraging boundary conditions from collinear and multi-Regge limits, and successfully applies it up to four loops for MHV amplitudes.

Contribution

It introduces a novel bootstrap method constrained by boundary data to compute scattering amplitudes without directly integrating, extending results to four loops for MHV and three loops for non-MHV cases.

Findings

Successfully computed six-gluon amplitudes up to four loops for MHV.

Extended the bootstrap to three loops for non-MHV amplitudes.

Demonstrated the effectiveness of boundary constraints in amplitude calculations.

Abstract

We describe the hexagon function bootstrap for solving for six-gluon scattering amplitudes in the large $N_c$ limit of ${\cal N}=4$ super-Yang-Mills theory. In this method, an ansatz for the finite part of these amplitudes is constrained at the level of amplitudes, not integrands, using boundary information. In the near-collinear limit, the dual picture of the amplitudes as Wilson loops leads to an operator product expansion which has been solved using integrability by Basso, Sever and Vieira. Factorization of the amplitudes in the multi-Regge limit provides additional boundary data. This bootstrap has been applied successfully through four loops for the maximally helicity violating (MHV) configuration of gluon helicities, and through three loops for the non-MHV case.