Non-planar on-shell diagrams

Franco, Sebastián; Galloni, Daniele; Penante, Brenda; Wen, Congkao

Abstract

We initiate a systematic study of non-planar on-shell diagrams in N=4 SYM and develop powerful technology for doing so. We introduce canonical variables generalizing face variables, which make the d log form of the on-shell form explicit. We make significant progress towards a general classification of arbitrary on-shell diagrams by means of two classes of combinatorial objects: generalized matching and matroid polytopes. We propose a boundary measurement that connects general on-shell diagrams to the Grassmannian. Our proposal exhibits two important and non-trivial properties: positivity in the planar case and it matches the combinatorial description of the diagrams in terms of generalized matroid polytopes. Interestingly, non-planar diagrams exhibit novel phenomena, such as the emergence of constraints on Plücker coordinates beyond Plücker relations when deleting edges, which are neatly captured by the generalized matching and matroid polytopes. This behavior is tied to the existence of a new type of poles in the on-shell form at which combinations of Plücker coordinates vanish. Finally, we introduce a prescription, applicable beyond the MHV case, for writing the on-shell form as a function of minors directly from the graph.

Citation

Franco, S., Galloni, D., Penante, B., & Wen, C. (2015). Non-planar on-shell diagrams. Journal of High Energy Physics, 2015(6), Article 199. https://doi.org/10.1007/jhep06%282015%29199

• Journal Article Type: Article
• Acceptance Date: Jun 10, 2015
• Online Publication Date: Jun 29, 2015
• Publication Date: Jun 30, 2015
• Deposit Date: Apr 23, 2019
• Publicly Available Date: Apr 23, 2019
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2015
• Issue: 6
• Article Number: 199
• DOI: https://doi.org/10.1007/jhep06%282015%29199