Local Spacetime Physics from the Grassmannian

Understand

A duality has recently been conjectured between all leading singularities of n-particle N^(k-2)MHV scattering amplitudes in N=4 SYM and the residues of a contour integral with a natural measure over the Grassmannian G(k,n).

• In this note we show that a simple contour deformation converts the sum of Grassmannian residues associated with the BCFW expansion of NMHV tree amplitudes to the CSW expansion of the same amplitude.
• We propose that for general k the same deformation yields the (k-2) parameter Risager expansion.
• We establish this equivalence for all MHV-bar amplitudes and show that the Risager degrees of freedom are non-trivially determined by the GL(k-2) "gauge" degrees of freedom in the Grassmannian.