Stratifying on-shell cluster varieties: the geometry of non-planar on-shell diagrams

Jacob L. Bourjaily, Sebastián Franco, Daniele Galloni, Congkao Wen

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30 Scopus citations


The correspondence between on-shell diagrams in maximally supersymmetric Yang-Mills theory and cluster varieties in the Grassmannian remains largely unexplored beyond the planar limit. In this article, we describe a systematic program to survey such ‘on-shell varieties’, and use this to provide a complete classification in the case of G(3, 6). In particular, we find exactly 24 top-dimensional varieties and 10 co-dimension one varieties in G(3, 6) — up to parity and relabeling of the external legs. We use this case to illustrate some of the novelties found for non-planar varieties relative to the case of positroids, and describe some of the features that we expect to hold more generally.

Original languageEnglish (US)
Article number3
JournalJournal of High Energy Physics
Issue number10
StatePublished - Oct 1 2016

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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