2009/12/07 by Jared Kaplan · 4 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Combinatorics #Grassmannian #Gravitational singularity #Kinematics #Loop (graph theory) #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Singularity #Topology (electrical circuits) #hep-th
paper · pdf · doi:10.1007/jhep03(2010)025
26+11 pages
arxiv created 2009/12/07 · openalex publication_date 2010/03/01 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.