Causality, Renormalizability and Ultra-High Energy Gravitational Scattering

TL;DR

This paper investigates how causality in ultra-high energy gravitational scattering relates to the renormalizability of quantum field theories, using Penrose limit techniques to analyze the energy dependence of scattering phase shifts.

Contribution

It introduces a method to compute the full energy dependence of the scattering phase shift in various scalar QFTs and clarifies the connection between causality and UV completion.

Findings

Causality violation correlates with the lack of a UV complete theory.

High-energy phase shifts reveal causality constraints in scalar QFTs.

String theory may resolve causality issues in gravitational scattering.

Abstract

The amplitude A(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 Theta_scat(hat_s},, where the single variable hat_s = 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 Theta_scat(hat_s) 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.