Holonomic representation of biadjoint scalar amplitudes

TL;DR

This paper introduces a novel holonomic representation of tree-level biadjoint scalar amplitudes using $D$-modules, capturing their pole and recursive properties through linear PDEs.

Contribution

It constructs left ideals in the Weyl algebra to represent amplitudes as solutions to holonomic systems, a new approach in the study of biadjoint scalar amplitudes.

Findings

Holonomic PDE systems encode amplitude properties

Representation captures pole and recursive structures

Provides a new algebraic framework for amplitudes

Abstract

We study tree-level biadjoint scalar amplitudes in the language of $D$-modules. We construct left ideals in the Weyl algebra $D$ that allow a holonomic representation of $n$-point amplitudes in terms of the linear partial differential equations they satisfy. The resulting representation encodes the simple pole and recursive properties of the amplitude.