$$ \mathcal{N} $$ = 7 On-shell diagrams and supergravity amplitudes in momentum twistor space

Abstract

We derive an on-shell diagram recursion for tree-level scattering amplitudes in $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 7 R-invariants analogous to those of $$ \mathcal{N} $$ 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.

Towards the Gravituhedron: new expressions for NMHV gravity amplitudes

“…The recursion relations have been also studied in the context of gravity on-shell diagrams [99,[116][117][118]. In the Yang-Mills case, the on-shell diagrams directly serve as building blocks for tree-level amplitudes and BCFW recursion relations are implemented diagrammatically [12].…”

“…In the Yang-Mills case, the on-shell diagrams directly serve as building blocks for tree-level amplitudes and BCFW recursion relations are implemented diagrammatically [12]. In gravity the due to the dimensionality of the coupling constant on-shell diagrams (calculated as cuts of loop integrands and given by the products of tree amplitudes) must be decorated by additional kinematical factors to be used for tree-level amplitudes via BCFW recursion relations [116,118], Inspired by both the KLT formula and the BCFW recursion relations, Elvang and Freedman found another MHV formula [119]…”

“…Note there are no double poles in this formula and it manifests O(1/z 2 ) behavior for certain shifts (more on this later). The same expression was also obtained using decorated gravity on-shell diagrams [118] and momentum twistor variables (for a particular ordering) were used to expose spurious poles cancelations.…”

“…Of course, we still have to sum them to get correct factorization on all physical poles. It would be interesting to understand if it is somehow related to three coordinate patches (in momentum twistor space) discussed in [118] which helped to understand the web of cancelations for N = 7 BCFW terms.…”

“…The use of momentum twistors for graviton amplitudes was proposed in [115] and then discussed in great details in [118] with some non-trivial results. The obvious problem is that momentum twistors require an ordering of external legs, hence they are very suitable for color-ordered gluon amplitudes.…”