### Abstract

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^{2}MHV 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.

Original language | English (US) |
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Article number | 49 |

Journal | Journal of High Energy Physics |

Volume | 2011 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2011 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2011*(1), [49]. https://doi.org/10.1007/JHEP01(2011)049