Bonus scaling and BCFW inN=7supergravity

Abstract

In search of natural building blocks for supergravity amplitudes, a tentative criteria is term-by-term bonus z^-2 large momentum scaling. For a given choice of deformation legs, we present such an expansion in the form of a BCFW representation in N=7 supergravity based on a special shift. We will show that this improved scaling behavior, with respect to the fully N=8 representation, is due to its automatic incorporation of the so called bonus relations.Comment: 16 pages, 2 figure

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

“…instead of (n − 2)! terms so it appears that the N = 7 recursion encodes bonus relations [27], as was previously observed in [28]. In [30], the bonus relations were used to write non-MHV amplitudes in N = 8 sugra as a sum over (n − 3)!…”

“…For example, for MHV amplitudes there are (n−3)! diagrams rather than (n−2)!, so the N = 7 recursion incorporates a property of sugra amplitudes known as the bonus relations [27] (this property of N = 7 recursion was first observed in [28]). 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.…”