TY - JOUR

T1 - Local spacetime physics from the Grassmannian

AU - Arkani-Hamed, N.

AU - Bourjaily, J.

AU - Cachazo, F.

AU - Trnka, J.

PY - 2011/9/28

Y1 - 2011/9/28

N2 - A duality has recently been conjectured between all leading singularities of n-particle Nk-2MHV 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 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. The Risager expansion is known to recursively construct the CSW expansion for all tree amplitudes, and given that the CSW expansion follows directly from the (super) Yang-Mills Lagrangian in light-cone gauge, this contour deformation allows us to directly see the emergence of local space-time physics from the Grassmannian.

AB - A duality has recently been conjectured between all leading singularities of n-particle Nk-2MHV 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 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. The Risager expansion is known to recursively construct the CSW expansion for all tree amplitudes, and given that the CSW expansion follows directly from the (super) Yang-Mills Lagrangian in light-cone gauge, this contour deformation allows us to directly see the emergence of local space-time physics from the Grassmannian.

UR - http://www.scopus.com/inward/record.url?scp=80053121574&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053121574&partnerID=8YFLogxK

U2 - 10.1007/JHEP01(2011)108

DO - 10.1007/JHEP01(2011)108

M3 - Article

AN - SCOPUS:80053121574

VL - 2011

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 1

M1 - 108

ER -