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

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 -