A study in \(\mathbb{G}_{\mathbb{R} , \geq 0} ( 2 , 6 )\): from the geometric case book of Wilson loop diagrams and SYM \(N =4\)

DOI10.4171/AIHPD/133MaRDI QIDQ2693189

Susama Agarwala, Siân Zee Friar

Publication date: 17 March 2023

Published in: Annales de l'Institut Henri Poincaré D. Combinatorics, Physics and their Interactions (AIHPD) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.00958

zbMATH Keywords

positive GrassmanniansSeodhar decompositionSYM \(N=4\)

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Supersymmetry and quantum mechanics (81Q60) Cluster algebras (13F60)

Uses Software

• SageMath
• SymPy

Cites Work

• Eliminating spurious poles from gauge-theoretic amplitudes
• Twistor-strings, Grassmannians and leading singularities
• Wilson loop diagrams and positroids
• A graph theoretic method for determining generating sets of prime ideals in quantum matrices
• Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves.
• From twistor actions to MHV diagrams
• Wilson loops in SYM \(\mathcal{N}=4\) do not parametrize an orientable space
• Decompositions of amplituhedra
• Matching polytopes, toric geometry, and the totally non-negative Grassmannian.
• Discrete Morse theory for totally non-negative flag varieties
• The twistor Wilson loop and the amplituhedron
• The correlahedron
• Unwinding the amplituhedron in binary
• The amplituhedron
• Positroids and non-crossing partitions
• A Formula for Plucker Coordinates Associated with a Planar Network
• Combinatorics of the geometry of Wilson loop diagrams II: Grassmann necklaces, dimensions, and denominators
• Combinatorics of the geometry of Wilson loop diagrams I: equivalence classes via matroids and polytopes
• AN ALGORITHM TO CONSTRUCT THE LE DIAGRAM ASSOCIATED TO A GRASSMANN NECKLACE
• The $m=1$ Amplituhedron and Cyclic Hyperplane Arrangements
• The totally nonnegative Grassmannian is a ball

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