Abstract
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.
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Bourjaily, J.L., Franco, S., Galloni, D. et al. Stratifying on-shell cluster varieties: the geometry of non-planar on-shell diagrams. J. High Energ. Phys. 2016, 3 (2016). https://doi.org/10.1007/JHEP10(2016)003
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DOI: https://doi.org/10.1007/JHEP10(2016)003