Gravitons, Bose-symmetry, and Bonus-scaling

Abstract

Modern on-shell S-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 Ref.~\cite{ST} that the recursion relations of Britto, Cachazo, Feng, and Witten (BCFW) apply to General Relativity tree amplitudes. We do so by showing that the surprising requirement of "bonus" $z^{-2}$ 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 $z^{\mathrm{even}}$. When applied to the color ordered expansions of Yang-Mills, this directly implies the improved behavior under non-adjacent gluon shifts. Using the same analysis, three-dimensional gravity amplitudes scale as $z^{-4}$, compared to the $z^{-1}$ behavior for conformal Chern-Simons matter theory.

arXiv comment6 pages

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Cited by in corpus (9)

• UV considerations on scattering amplitudes in a web of theories
• Ultralight Fermionic Dark Matter
• Hidden zeros are equivalent to enhanced ultraviolet scaling and lead to unique amplitudes in Tr(${\varphi }^3$) theory
• Uniqueness from locality and BCFW shifts
• Hidden Conformal Symmetry in Tree-Level Graviton Scattering
• Gravity loop integrands from the ultraviolet
• UV consistency conditions for CHY integrands
• From U(1) to E8: soft theorems in supergravity amplitudes
• Bonus scaling and BCFW in N=7 supergravity