Cluster Functions and Scattering Amplitudes for Six and Seven Points

TL;DR

This paper investigates the mathematical structure of six- and seven-point scattering amplitudes in super-Yang-Mills theory, focusing on cluster algebra functions and their role in constraining amplitude calculations.

Contribution

It provides a comprehensive classification of cluster polylogarithm functions relevant for two-loop six- and seven-point amplitudes, enhancing the bootstrap approach.

Findings

Complete taxonomy of Gr(4,6) and Gr(4,7) cluster functions at weight 4

Quantitative analysis of physical and mathematical constraints on amplitudes

Insights into the intersection of physical principles and cluster algebra structures

Abstract

Scattering amplitudes in planar super-Yang-Mills theory satisfy several basic physical and mathematical constraints, including physical constraints on their branch cut structure and various empirically discovered connections to the mathematics of cluster algebras. The power of the bootstrap program for amplitudes is inversely proportional to the size of the intersection between these physical and mathematical constraints: ideally we would like a list of constraints which determine scattering amplitudes uniquely. We explore this intersection quantitatively for two-loop six- and seven-point amplitudes by providing a complete taxonomy of the Gr(4,6) and Gr(4,7) cluster polylogarithm functions of arXiv:1401.6446 at weight 4.