Causality in the presence of stacked shockwaves

Relativistic causality constrains the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi></a:math>-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, semiclassical, and Born approximations. We apply this to the effective field theory 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. Phrased the other way, this can be read as a bound on the Wilson coefficient from infrared causality which are consistent with positivity/bootstrap bounds.