TY - JOUR
T1 - Stratifying on-shell cluster varieties: the geometry of non-planar on-shell diagrams
AU - Bourjaily, Jacob Lewis
AU - Franco, Sebastián
AU - Galloni, Daniele
AU - Wen, Congkao
PY - 2016/10/1
Y1 - 2016/10/1
N2 - 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.
AB - 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.
U2 - 10.1007/JHEP10(2016)003
DO - 10.1007/JHEP10(2016)003
M3 - Journal article
SN - 1126-6708
VL - 2016
JO - Journal of High Energy Physics (Online)
JF - Journal of High Energy Physics (Online)
IS - 10
ER -