Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-02-05
JHEP 0711:057,2007
Physics
High Energy Physics
High Energy Physics - Theory
29 pages, v2: statement in the introduction corrected, appendix B added, reference added, JHEP style
Scientific paper
10.1088/1126-6708/2007/11/057
We give a proof of BCFW recursion relations for all tree-level amplitudes of gravitons in General Relativity. The proof follows the same basic steps as in the BCFW construction and it is an extension of the one given for next-to-MHV amplitudes by one of the authors and P. Svr\v{c}ek in hep-th/0502160. The main obstacle to overcome is to prove that deformed graviton amplitudes vanish as the complex variable parameterizing the deformation is taken to infinity. This step is done by first proving an auxiliary recursion relation where the vanishing at infinity follows directly from a Feynman diagram analysis. The auxiliary recursion relation gives rise to a representation of gravity amplitudes where the vanishing under the BCFW deformation can be directly proven. Since all our steps are based only on Feynman diagrams, our proof completely establishes the validity of BCFW recursion relations. This means that many results in the literature that were derived assuming their validity become true statements.
Benincasa Paolo
Boucher-Veronneau Camille
Cachazo Freddy
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