Abstract
We derive an on-shell diagram recursion for tree-level scattering amplitudes in mathcal{N} = 7 supergravity. The diagrams are evaluated in terms of Grassmannian integrals and momentum twistors, generalising previous results of Hodges in momentum twistor space to non-MHV amplitudes. In particular, we recast five and six-point NMHV amplitudes in terms of mathcal{N} = 7 R-invariants analogous to those of mathcal{N} = 4 super-Yang-Mills, which makes cancellation of spurious poles more transparent. Above 5-points, this requires defining momentum twistors with respect to different orderings of the external momenta.
Highlights
Was extended to all NMHV amplitudes in N = 4 SYM in [4], where an amplitude with k negative helicity particles is referred to as Nk−2MHV. Another important perspective came from on-shell diagrams [5], which provide a diagrammatic representation of BCFW recursion [6,7,8] and give rise to Grassmannian integral formulas
The relation between twistor string and on-shell diagram diescriptions of N = 8 sugra amplitudes was explored in [26], where a Grassmannian integral formula for the 6-point NMHV amplitude was obtained for the first time
The price to pay for having fewer diagrams is that they generally contain more closed cycles which can become tedious to evaluate at high multiplicity using conventional methods, so we develop a new technique which avoids summing over closed cycles
Summary
First we review some standard notation for scattering amplitudes. A null momentum in four dimensions can be expressed in the following bi-spinor form: pαi α = λαi λαi ,. On-shell diagrams provide a diagrammatic representation of BCFW recursion They are built out of black and white vertices denoting MHV and MHV amplitudes respectively, which are connected by lines representing an integral over on-shell states. This was first developed for planar N = 4 SYM [5] and later generalised to tree-level amplitudes of N = 8 sugra [19]. These can be obtained by decorating planar on-shell diagrams and summing over permutations of unshifted legs, giving (n − 2)! We are free to move decorations to the opposite edge of a box, which can be seen from the definition in (2.13)
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