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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.


This article was originally published in the Journal of High Energy Physics, available at doi:10.1007/JHEP10(2016)003.

This article is distributed under the terms of the Creative Commons Attribution License (CC BY 4.0).

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