Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-12-30
JHEP 1101:049,2011
Physics
High Energy Physics
High Energy Physics - Theory
56 pages, 11 figures; v2: typos corrected, minor improvements
Scientific paper
10.1007/JHEP01(2011)049
The conjectured duality relating all-loop leading singularities of n-particle N^(k-2)MHV scattering amplitudes in N=4 SYM to a simple contour integral over the Grassmannian G(k,n) makes all the symmetries of the theory manifest. Every residue is individually Yangian invariant, but does not have a local space-time interpretation--only a special sum over residues gives physical amplitudes. In this paper we show that the sum over residues giving tree amplitudes can be unified into a single algebraic variety, which we explicitly construct for all NMHV and N^2MHV amplitudes. Remarkably, this allows the contour integral to have a "particle interpretation" in the Grassmannian, where higher-point amplitudes can be constructed from lower-point ones by adding one particle at a time, with soft limits manifest. We move on to show that the connected prescription for tree amplitudes in Witten's twistor string theory also admits a Grassmannian particle interpretation, where the integral over the Grassmannian localizes over the Veronese map from G(2,n) to G(k,n). These apparently very different theories are related by a natural deformation with a parameter t that smoothly interpolates between them. For NMHV amplitudes, we use a simple residue theorem to prove t-independence of the result, thus establishing a novel kind of duality between these theories.
Arkani-Hamed Nima
Bourjaily Jacob
Cachazo Freddy
Trnka Jaroslav
No associations
LandOfFree
Unification of Residues and Grassmannian Dualities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Unification of Residues and Grassmannian Dualities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Unification of Residues and Grassmannian Dualities will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-103325