A new symplectic bi-Grassmannian representation encodes CFT4 Wightman correlators via integrals over mutually symplectically orthogonal n-planes aligned with kinematics, reproducing known 2- and 3-point structures compactly and revealing double-copy properties.
A Duality For The S Matrix
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abstract
We propose a dual formulation for the S Matrix of N = 4 SYM. The dual provides a basis for the "leading singularities" of scattering amplitudes to all orders in perturbation theory, which are sharply defined, IR safe data that uniquely determine the full amplitudes at tree level and 1-loop, and are conjectured to do so at all loop orders. The scattering amplitude for n particles in the sector with k negative helicity gluons is associated with a simple integral over the space of k planes in n dimensions, with the action of parity and cyclic symmetries manifest. The residues of the integrand compute a basis for the leading singularities. A given leading singularity is associated with a particular choice of integration contour, which we explicitly identify at tree level and 1-loop for all NMHV amplitudes as well as the 8 particle NNMHV amplitude. We also identify a number of 2-loop leading singularities for up to 8 particles. There are a large number of relations among residues which follow from the multi-variable generalization of Cauchy's theorem known as the "global residue theorem". These relations imply highly non-trivial identities guaranteeing the equivalence of many different representations of the same amplitude. They also enforce the cancellation of non-local poles as well as consistent infrared structure at loop level. Our conjecture connects the physics of scattering amplitudes to a particular subvariety in a Grassmannian; space-time locality is reflected in the topological properties of this space.
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Derives expansion formulas for multi-trace YMS amplitudes bottom-up from soft gluon and scalar behaviors.
Tree-level N=2 super wavefunction coefficients are written in orthogonal-Grassmannian form by inverting a basis of energy discontinuities and embedding them in momentum superspace.
Explicit three-loop computation of negative geometries for F(g,z) with all-loop resummation of one-cycle diagrams and extraction of the cusp anomalous dimension via z-integration.
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The Conformal Grassmannian: A Symplectic Bi-Grassmannian for $CFT_ 4$ Correlators
A new symplectic bi-Grassmannian representation encodes CFT4 Wightman correlators via integrals over mutually symplectically orthogonal n-planes aligned with kinematics, reproducing known 2- and 3-point structures compactly and revealing double-copy properties.
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Multi-trace YMS amplitudes from soft behavior
Derives expansion formulas for multi-trace YMS amplitudes bottom-up from soft gluon and scalar behaviors.
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Beyond Discontinuities: Cosmological WFCs and the Supersymmetric Orthogonal Grassmannian
Tree-level N=2 super wavefunction coefficients are written in orthogonal-Grassmannian form by inverting a basis of energy discontinuities and embedding them in momentum superspace.
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Multi-Loop Negative Geometries
Explicit three-loop computation of negative geometries for F(g,z) with all-loop resummation of one-cycle diagrams and extraction of the cusp anomalous dimension via z-integration.