Positroids, Plabic Graphs, and Scattering Amplitudes in Mathematica

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.

24 pages, 9 figures. Included with the submission is the Mathematica package "positroids" and a notebook with many detailed examples

References in corpus (6)

• Total positivity, Grassmannians, and networks
• Sharpening The Leading Singularity
• All tree-level amplitudes in massless QCD
• The Grassmannian and the Twistor String: Connecting All Trees in N=4 SYM
• On the structure of scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity
• Efficient Tree-Amplitudes in N=4: Automatic BCFW Recursion in Mathematica

Cited by in corpus (2)

• Dual-Conformal Regularization of Infrared Loop Divergences and the Chiral Box Expansion
• Brane Tilings as On-shell Diagrams