Research Paper#Theoretical Physics, Scattering Amplitudes, Gauge Theory, Grassmannian Geometry🔬 ResearchAnalyzed: Jan 3, 2026 06:15
Grassmannian Geometries for Non-Planar On-Shell Diagrams
Published:Dec 31, 2025 17:53
•1 min read
•ArXiv
Analysis
This paper explores non-planar on-shell diagrams in the context of scattering amplitudes, a topic relevant to understanding gauge theories like N=4 Super Yang-Mills. It extends the well-studied planar diagrams to the more complex non-planar case, which is important at finite N. The paper uses the Grassmannian formalism and identifies specific geometric structures (pseudo-positive geometries) associated with these diagrams. The work contributes to the mathematical understanding of scattering amplitudes and provides insights into the behavior of gauge theories beyond the large N limit.
Key Takeaways
- •Focuses on non-planar on-shell diagrams, relevant at finite N.
- •Uses the Grassmannian formalism to analyze these diagrams.
- •Identifies pseudo-positive geometries associated with MHV diagrams.
- •Proves completeness of identity moves for MHV on-shell diagrams.
Reference
“The paper shows that non-planar diagrams, specifically MHV diagrams, can be represented by pseudo-positive geometries in the Grassmannian G(2,n).”