Taming tree amplitudes in general relativity

By Paolo Benincasa, C. Boucher-Veronneau, F. Cachazo. 2007

152 citations recorded by the source corpus.

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. Svrcek 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c3553a27e74f2c2c4072f6a735dfb5ae9248aadc

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Citations in the corpus

TASI Lectures on Scattering Amplitudes (2017, background): “Remarkably, the BCFW recursion relations are also applicable to graviton scattering amplitudes [52].”
The Cosmological Optical Theorem (2020, background): “In fact, one of the greatest achievements of the amplitude program is the on-shell construction of all tree level amplitudes of YM and GR [48, 49, 50, 51, 52].”
Evidence for a New Soft Graviton Theorem (2014, background): “(30) There are several proofs in the literature [19, 20] that Mn+1(z) → 1/z as z → ∞.”
Loop corrections to soft theorems in gauge theories and gravity (2014, unknown): “M (1) 4 (1 , 2, 3, 4) = 1 180 ( st u [24]2 [12]〈23〉[34]〈41〉 )2 (s(2) + t(2) + st) .”
Generating tree amplitudes in Script N = 4 SYM and Script N = 8 SG (2008, background): “Cachazo et al provided in [26] the first proof of the validity of the 2-line recursion relations for graviton amplitudes.”