Surfin' pp-waves with Good Vibrations: Causality in the presence of stacked shockwaves

TL;DR

This paper investigates causality constraints in relativistic scattering within stacked shockwave spacetimes, demonstrating that effective field theory corrections remain unresolvable and consistent with positivity bounds, ensuring infrared causality.

Contribution

It provides a detailed analysis of scattering time delays in pp-wave spacetimes with stacked shockwaves, extending causality bounds to higher-dimensional gravity EFTs.

Findings

Corrections to time delays are generally unresolvable within EFT validity.

Results align with positivity bounds and causality constraints.

Higher-dimensional operators do not violate causality in the studied regime.

Abstract

Relativistic causality constrains the $S$-matrix both through its analyticity, and by imposing lower bounds on the scattering time delay. These bounds are easiest to determine for spacetimes which admit either a timelike or null Killing vector. We revisit a class of pp-wave spacetimes and carefully determine the scattering time delay for arbitrary incoming states in the eikonal, semi-classical, and Born approximations. We apply this to the EFT of gravity in arbitrary dimensions. It is well-known that higher-dimension operators such as the Gauss-Bonnet term, when treated perturbatively at low energies, can appear to make both positive and negative contributions to the time delays of the background geometry. We show that even when multiple shockwaves are stacked, the corrections to the scattering time delay relative to the background are generically unresolvable within the regime of validity of the effective field theory so long as the Wilson coefficients are of order unity. This is in agreement with previously derived positivity/bootstrap bounds and the requirement that infrared causality be maintained in consistent low-energy effective theories, irrespective of the UV completion.