Taming Tree Amplitudes In General Relativity
Paolo Benincasa, Camille Boucher-Veronneau, Freddy Cachazo
TL;DR
The paper proves that tree-level graviton amplitudes in General Relativity obey BCFW recursion relations by constructing an auxiliary maximal-deformation recursion that yields M_n(w) → 0 at infinity. Combining this with a standard BCFW deformation, the authors derive a complete, on-shell factorization-based representation of gravity amplitudes in terms of lower-point amplitudes. This establishes the formal validity of BCFW in gravity and supports prior results that relied on its assumed existence, while Ward identities extend the framework to additional deformation schemes. The work clarifies why individual Feynman diagrams diverge but the full amplitudes cancel, and it highlights potential connections to deeper structures such as twistor-inspired formulations and no-triangle-type simplifications in gravity amplitudes.
Abstract
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. Svrček 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.