Unraveling L_{n,k}: Grassmannian Kinematics

Abstract

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 very 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 a special case we consider a 12-pt N^4MHV leading singularity at two loops that has a new 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.

26+11 pages

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• Gluon scattering amplitudes at strong coupling
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Cited by in corpus (35)

• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Towards a Basis for Planar Two-Loop Integrals
• Unification of Residues and Grassmannian Dualities
• Yangians, Grassmannians and T-duality
• The Yangian origin of the Grassmannian integral
• Scattering Amplitudes and Wilson Loops in Twistor Space
• Bipartite Field Theories: from D-Brane Probes to Scattering Amplitudes
• Superconformal invariants for scattering amplitudes in N=4 SYM theory
• Twistor-Strings, Grassmannians and Leading Singularities
• MHV Diagrams in Momentum Twistor Space
• Local Spacetime Physics from the Grassmannian
• Simple loop integrals and amplitudes in N=4 SYM
• An Introduction to On-shell Recursion Relations
• The Grassmannian and the Twistor String: Connecting All Trees in N=4 SYM
• A First Course on Twistors, Integrability and Gluon Scattering Amplitudes
• Stratifying On-Shell Cluster Varieties: the Geometry of Non-Planar On-Shell Diagrams
• Positroids, Plabic Graphs, and Scattering Amplitudes in Mathematica
• Efficient Tree-Amplitudes in N=4: Automatic BCFW Recursion in Mathematica
• Descent equations for superamplitudes
• A Grassmannian Etude in NMHV Minors
• Inverse Soft Factors and Grassmannian Residues
• On-shell diagrams and the geometry of planar N < 4 SYM theories
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• On the Classification of Residues of the Grassmannian
• Positivity Sectors and the Amplituhedron
• Scattering amplitudes at strong coupling for 4K gluons
• Non-Planar On-Shell Diagrams
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Anatomy of the Amplituhedron
• Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory
• Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes
• Illustrations of Integrand-Basis Building at Two Loops
• All Two-Loop, Color-Dressed, Six-Point Amplitude Integrands in sYM
• Energy-Energy Correlator from the AdS Virasoro-Shapiro Amplitude
• On the Integrable Structure of Super Yang-Mills Scattering Amplitudes