Abstract
Modern on-shell -matrix methods may dramatically improve our understanding of perturbative quantum gravity, but current foundations of on-shell techniques for general relativity still rely on off-shell Feynman diagram analysis. Here, we complete the fully on-shell proof of Schuster and Toro J. High Energy Phys. 06 (2009) 079] that the recursion relations of Britto, Cachazo, Feng, and Witten (BCFW) apply to relativity tree amplitudes. We do so by showing that the surprising requirement of “bonus” scaling under a BCFW shift directly follows from Bose symmetry. Moreover, we show that amplitudes in generic theories subjected to BCFW deformations of identical particles necessarily scale as . When applied to the color ordered expansions of Yang-Mills, this directly implies the improved behavior under nonadjacent gluon shifts. Using the same analysis, three-dimensional gravity amplitudes scale as , compared to the behavior for conformal Chern-Simons matter theory.
- Received 16 December 2014
DOI:https://doi.org/10.1103/PhysRevD.91.105010
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