Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 1, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP01(2011)049
Keywords
Supersymmetry and Duality; Supersymmetric gauge theory; Extended Supersymmetry; String Duality
Categories
Funding
- DOE [DE-FG02-91ER40654]
- NSERC of Canada
- MEDT of Ontario
- The Ambrose Monell Foundation
- U.S. Department of State
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The conjectured duality relating all-loop leading singularities of n-particle Nk-2MHV 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 (NMHV)-M-2 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) -> 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.
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