Causality, renormalizability and ultra-high energy gravitational scattering

The amplitude  ( s , t ) for ultra-high energy scattering can be found in the leading eikonal approximation by considering propagation in an Aichelburg–Sexl gravitational shockwave background. Loop corrections in the QFT describing the scattered particles are encoded for energies below the Planck scale in an effective action which in general exhibits causality violation and Shapiro time advances. In this paper, we use Penrose limit techniques to calculate the full energy dependence of the scattering phase shift Θ scat ( s ˆ ) , where the single variable s ˆ = Gs / m 2 b d − 2 contains both the CM energy s and impact parameter b, for a range of scalar QFTs in d dimensions with different renormalizability properties. We evaluate the high-energy limit of Θ scat ( s ˆ ) and show in detail how causality is related to the existence of a well-defined UV completion. Similarities with graviton scattering and the corresponding resolution of causality violation in the effective action by string theory are briefly discussed.