Singularities of massless scattering and cluster algebras

TL;DR

This paper investigates the role of cluster algebras associated with partial flag varieties in understanding massless scattering amplitudes, revealing that these algebraic structures encode key information about symbol alphabets at five and six points.

Contribution

It provides evidence that cluster algebras from partial flag varieties contain relevant information for massless scattering amplitudes, highlighting differences between spinor-helicity and momentum twistor structures.

Findings

Cluster algebras encode symbol alphabet information for five and six-point scattering.

Momentum twistor structures capture a larger alphabet subset than spinor-helicity at six points.

Cluster structures predict the appearance of certain symbol letter triples related to mutation relations.

Abstract

Partial flag varieties arise in the context of massless scattering kinematics. They can be associated to both spinor-helicity variables and momentum twistor variables in two separate yet natural ways. Here we report on evidence at five and six points that the cluster algebras associated to these partial flag varieties contain information relevant to non-dual conformal massless scattering amplitudes and related observables. At five points both spinor-helicity and momentum twistor cluster structures capture similar information about symbol alphabets. At six points we demonstrate that the momentum twistor structure captures a larger subset of the alphabet compared to the spinor-helicity one. We also observe that the associated cluster structures correctly predict the appearance of certain triples of symbol letters related to cluster mutation relations.