Unraveling L_{n,k}: Grassmannian Kinematics

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It was recently proposed that the leading singularities of the S-Matrix of 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 N{sup ... continued below

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37 pages

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Kaplan, Jared & /SLAC February 15, 2010.

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It was recently proposed that the leading singularities of the S-Matrix of 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 N{sup 4}MHV 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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37 pages

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  • Journal Name: Submitted to Journal of High Energy Physics (JHEP)

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  • Report No.: SLAC-PUB-13870
  • Grant Number: AC02-76SF00515
  • DOI: 10.1007/JHEP03(2010)025 | External Link
  • Office of Scientific & Technical Information Report Number: 972257
  • Archival Resource Key: ark:/67531/metadc934481

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  • February 15, 2010

Added to The UNT Digital Library

  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 15, 2016, 3:34 p.m.

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Kaplan, Jared & /SLAC. Unraveling L_{n,k}: Grassmannian Kinematics, article, February 15, 2010; United States. (digital.library.unt.edu/ark:/67531/metadc934481/: accessed August 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.