Positroids, Plabic Graphs, and Scattering Amplitudes in Mathematica

TL;DR

This paper introduces a Mathematica package called 'positroids' that provides tools for exploring the connections between scattering amplitudes, on-shell diagrams, and positroid stratification of the Grassmannian, facilitating research in this area.

Contribution

The paper presents a new Mathematica package that simplifies the construction, visualization, and evaluation of positroid configurations and on-shell diagrams for scattering amplitudes.

Findings

Provides tools for constructing canonical coordinates for positroids

Includes functions for drawing on-shell (plabic) graphs

Enables evaluation of on-shell differential forms

Abstract

The many intricate connections between scattering amplitudes, on-shell diagrams, and the positroid stratification of the Grassmannian has recently been described in great detail. In order to facilitate the exploration of this rich correspondence, we have prepared a public Mathematica package called "positroids" which includes an array of useful tools including those for the construction of canonical coordinates for positroid configurations, the drawing of representative on-shell (plabic) graphs, and the evaluation of on-shell differential forms. This note documents the functions made available by the positroids package; the package's source code together with a Mathematica notebook containing many detailed examples of its functionality are included with this note's submission files on the arXiv.