On the Classification of Residues of the Grassmannian

Abstract

We study leading singularities of scattering amplitudes which are obtained as residues of an integral over a Grassmannian manifold. We recursively do the transformation from twistors to momentum twistors and obtain an iterative formula for Yangian invariants that involves a succession of dualized twistor variables. This turns out to be useful in addressing the problem of classifying the residues of the Grassmannian. The iterative formula leads naturally to new coordinates on the Grassmannian in terms of which both composite and non-composite residues appear on an equal footing. We write down residue theorems in these new variables and classify the independent residues for some simple examples. These variables also explicitly exhibit the distinct solutions one expects to find for a given set of vanishing minors from Schubert calculus.

20 pages

References in corpus (23)

• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• All tree-level amplitudes in N=4 SYM
• Taming Tree Amplitudes In General Relativity
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Sharpening The Leading Singularity
• Tree Level Recursion Relations In General Relativity
• The Yangian origin of the Grassmannian integral
• Loop amplitudes in gauge theories: modern analytic approaches
• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
• Eliminating spurious poles from gauge-theoretic amplitudes
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• Twistor diagram recursion for all gauge-theoretic tree amplitudes
• Scattering amplitudes for eight gauge fields
• Inverse Soft Factors and Grassmannian Residues

Cited by in corpus (5)

• Scattering Amplitudes and Wilson Loops in Twistor Space
• Cluster Adjacency for m=2 Yangian Invariants
• Yangian Invariants and Cluster Adjacency in N=4 Yang-Mills
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Weak Separation, Positivity and Extremal Yangian Invariants