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 (17)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• New Recursion Relations for Tree Amplitudes of Gluons
• What is the Simplest Quantum Field Theory?
• Total positivity, Grassmannians, and networks
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• On-Shell Methods in Perturbative QCD
• Unification of Residues and Grassmannian Dualities
• Computing One-Loop Amplitudes From The Holomorphic Anomaly Of Unitarity Cuts
• Generalized unitarity for N=4 super-amplitudes
• Sharpening The Leading Singularity
• All tree-level amplitudes in massless QCD
• Twistor-Strings, Grassmannians and Leading Singularities
• The Grassmannian and the Twistor String: Connecting All Trees in N=4 SYM
• Unraveling L_{n,k}: Grassmannian Kinematics
• 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 (20)

• Positive Amplitudes In The Amplituhedron
• The Momentum Amplituhedron
• Rationalizing Loop Integration
• On-shell Diagrams, Graßmannians and Integrability for Form Factors
• Notes on Scattering Amplitudes as Differential Forms
• All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
• Amplitudes at Infinity
• Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory
• Manifestly Dual-Conformal Loop Integration
• Building Bases of Loop Integrands
• A Note on Letters of Yangian Invariants
• Prescriptive Unitarity with Elliptic Leading Singularities
• Symbol Alphabets from Plabic Graphs II: Rational Letters
• An Elliptic Yangian-Invariant, `Leading Singularity'
• Boundaries of the Amplituhedron with amplituhedronBoundaries
• Dual-Conformal Regularization of Infrared Loop Divergences and the Chiral Box Expansion
• Positivity Sectors and the Amplituhedron
• The m=2 amplituhedron and the hypersimplex: signs, clusters, triangulations, Eulerian numbers
• Cyclicity of All Anti-NMHV and N${}^2$MHV Tree Amplitudes in N=4 SYM
• Brane Tilings as On-shell Diagrams