Positroid Stratification of Orthogonal Grassmannian and ABJM Amplitudes

Abstract

A novel understanding of scattering amplitudes in terms of on-shell diagrams and positive Grassmannian has been recently established for four dimensional Yang-Mills theories and three dimensional Chern-Simons theories of ABJM type. We give a detailed construction of the positroid stratification of orthogonal Grassmannian relevant for ABJM amplitudes. On-shell diagrams are classified by pairing of external particles. We introduce a combinatorial aid called `OG tableaux' and map each equivalence class of on-shell diagrams to a unique tableau. The on-shell diagrams related to each other through BCFW bridging are naturally grouped by the OG tableaux. Introducing suitably ordered BCFW bridges and positive coordinates, we construct the complete coordinate charts to cover the entire positive orthogonal Grassmannian for arbitrary number of external particles. The graded counting of OG tableaux suggests that the positive orthogonal Grassmannian constitutes a combinatorial polytope.

32 pages, 23 figures; v2. minor corrections; v3. several clarifications and minor improvements

References in corpus (8)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Scattering in Three Dimensions from Rational Maps
• Yangian Invariant Scattering Amplitudes in Supersymmetric Chern-Simons Theory
• Scattering in Mass-Deformed N>=4 Chern-Simons Models
• Dual Superconformal Symmetry of N=6 Chern-Simons Theory
• ABJM amplitudes and the positive orthogonal grassmannian
• Amplitudes of 3D and 6D Maximal Superconformal Theories in Supertwistor Space
• The Grassmannian and the Twistor String: Connecting All Trees in N=4 SYM

Cited by in corpus (7)

• Evidence for a Nonplanar Amplituhedron
• Gravity On-shell Diagrams
• Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4$ SYM and 3d ABJM
• Positive geometry, local triangulations, and the dual of the Amplituhedron
• On-shell diagrams and the geometry of planar N < 4 SYM theories
• On the geometry of the orthogonal momentum amplituhedron
• ABJM Amplitudes in U-gauge and a Soft Theorem