Abstract
It was recently proposed that the leading singularities of the S-Matrix of \(\mathcal N \) = 4 super Yang-Mills theory arise as the residues of a contour integral over a Grassmannian manifold, with space-time locality encoded through residue theorems generalizing Cauchy’s theorem to more than one variable. We provide a method to identify the residue corresponding to any leading singularity, and we carry this out explicitly for all leading singularities at tree level and one-loop. We also give several examples at higher loops, including all generic two-loop leading singularities and an interesting four-loop object. As an example we consider a 12-pt N4MHV leading singularity at two loops that has a kinematic structure involving double square roots. Our analysis results in a simple picture for how the topological structure of loop graphs is reflected in various substructures within the Grassmannian.
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Kaplan, J. Unraveling \(\mathcal {L}_{n, k} \): grassmannian kinematics. J. High Energ. Phys. 2010, 25 (2010). https://doi.org/10.1007/JHEP03(2010)025
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DOI: https://doi.org/10.1007/JHEP03(2010)025