Abstract
We continue the discussion of the decorated on-shell diagrammatics for planar \( \mathcal{N}<4 \) Supersymmetric Yang-Mills theories started in [1]. In particular, we focus on its relation with the structure of varieties on the Grassmannian. The decoration of the on-shell diagrams, which physically keeps tracks of the helicity of the coherent states propagating along their edges, defines new on-shell functions on the Grassmannian and can introduce novel higher-order singularities, which graphically are reflected into the presence of helicity loops in the diagrams. These new structures turn out to have similar features as in the non-planar case: the related higher-codimension varieties are identified by either the vanishing of one (or more) Plücker coordinates involving at least two non-adjacent columns, or new relations among Plücker coordinates. A distinctive feature is that the functions living on these higher-codimenson varieties can be thought of distributionally as having support on derivative delta-functions. After a general discussion, we explore in some detail the structures of the on-shell functions on Gr(2, 4) and Gr(3, 6) on which the residue theorem allows to obtain a plethora of identities among them.
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ArXiv ePrint: 1609.01923
‘La Caixa’-Severo Ochoa Scholar. (David Gordo)
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Benincasa, P., Gordo, D. On-shell diagrams and the geometry of planar \( \mathcal{N}<4 \) SYM theories. J. High Energ. Phys. 2017, 192 (2017). https://doi.org/10.1007/JHEP11(2017)192
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DOI: https://doi.org/10.1007/JHEP11(2017)192