Sebastián Franco
The geometry of on-shell diagrams
Franco, Sebastián; Galloni, Daniele; Mariotti, Alberto
Authors
Daniele Galloni
Alberto Mariotti
Abstract
The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such as the Grassmannian. We perform a detailed investigation of the combinatorial and geometric objects associated to these graphs. We mainly focus on their relation to polytopes and toric geometry, the Grassmannian and its stratification. Our work extends the current understanding of these connections along several important fronts, most notably eliminating restrictions imposed by planarity, positivity, reducibility and edge removability. We illustrate our ideas with several explicit examples and introduce concrete methods that considerably simplify computations. We consider it highly likely that the structures unveiled in this article will arise in the on-shell study of scattering amplitudes beyond the planar limit. Our results can be conversely regarded as an expansion in the understanding of the Grassmannian in terms of bipartite graphs.
Citation
Franco, S., Galloni, D., & Mariotti, A. (2014). The geometry of on-shell diagrams. Journal of High Energy Physics, 2014(8), Article 38. https://doi.org/10.1007/jhep08%282014%29038
Journal Article Type | Article |
---|---|
Publication Date | Jan 1, 2014 |
Deposit Date | Apr 26, 2019 |
Publicly Available Date | Apr 26, 2019 |
Journal | Journal of High Energy Physics |
Print ISSN | 1126-6708 |
Electronic ISSN | 1029-8479 |
Publisher | Scuola Internazionale Superiore di Studi Avanzati (SISSA) |
Peer Reviewed | Peer Reviewed |
Volume | 2014 |
Issue | 8 |
Article Number | 38 |
DOI | https://doi.org/10.1007/jhep08%282014%29038 |
Public URL | https://durham-repository.worktribe.com/output/1332281 |
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Copyright Statement
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
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