Classification of all 3 particle S-matrices quadratic in photons or gravitons

Abstract

We explicitly construct every kinematically allowed three particle graviton-graviton-$P$ and photon-photon-$P$ S-matrix in every dimension and for every choice of the little group representation of the massive particle $P$. We also explicitly construct the spacetime Lagrangian that generates each of these couplings. In the case of gravitons we demonstrate that this Lagrangian always involves (derivatives of) two factors of the Riemann tensor, and so is always of fourth or higher order in derivatives. This result verifies one of the assumptions made in the recent preprint \cite{Chowdhury:2019kaq} while attempting to establish the rigidity of the Einstein tree level S-matrix within the space of local classical theories coupled to a collection of particles of bounded spin.

arXiv commentadded references

References in corpus (11)

• Spinning Conformal Correlators
• xTras: a field-theory inspired xAct package for Mathematica
• Amplitudes and Spinor-Helicity in Six Dimensions
• Conformal correlators of mixed-symmetry tensors
• Projectors and seed conformal blocks for traceless mixed-symmetry tensors
• Bounds on Amplitudes in Effective Theories with Massive Spinning Particles
• Spinning operators and defects in conformal field theory
• Scalar-Vector Bootstrap
• Twist decomposition of nonlocal light-cone operators II: General tensors of 2nd rank
• Superfield integrals in high dimensions
• Massive Scattering Amplitudes in Six Dimensions

Cited by in corpus (8)

• Notes on flat-space limit of AdS/CFT
• Graviton partial waves and causality in higher dimensions
• Amplitude bases in generic EFTs
• Consistent actions for massive particles interacting with electromagnetism and gravity
• On-shell Supersymmetry and higher-spin amplitudes
• Spinning amplitudes from scalar amplitudes
• Five-point partial waves, splitting constraints and hidden zeros
• Three point interaction of Dirac fermions with higher spin particles and discrete symmetries