Electric shocks: bounding Einstein-Maxwell theory with time delays on boosted RN backgrounds

TL;DR

This paper investigates how causality constraints on particle propagation in curved backgrounds impose bounds on higher-derivative operators in Einstein-Maxwell theory, using shockwave backgrounds and time delay calculations.

Contribution

It extends positivity bounds from scalar and electromagnetic theories to charged gravitational shockwaves, analyzing the effects of gravity and higher-derivative corrections on causality constraints.

Findings

Positive time delay implies positivity of four-derivative operators in scalar and electromagnetic theories.

Gravity introduces a logarithmic term in the time delay, complicating straightforward bounds.

Methods to extract meaningful bounds include IR cutoff and derivative of the time delay.

Abstract

The requirement that particles propagate causally on non-trivial backgrounds implies interesting constraints on higher-derivative operators. This work is part of a systematic study of the positivity bounds derivable from time delays on shockwave backgrounds. First, we discuss shockwaves in field theory, which are infinitely boosted Coulomb-like field configurations. We show how a positive time delay implies positivity of four-derivative operators in scalar field theory and electromagnetism, consistent with the results derived using dispersion relations, and we comment on how additional higher-derivative operators could be included. We then turn to gravitational shockwave backgrounds. We compute the infinite boost limit of Reissner-Nordstr\"om black holes to derive charged shockwave backgrounds. We consider photons traveling on these backgrounds and interacting through four-derivative corrections to Einstein-Maxwell theory. The inclusion of gravity introduces a logarithmic term into the time delay that interferes with the straightforward bounds derivable in pure field theory, a fact consistent with CEMZ and with recent results from dispersion relations. We discuss two ways to extract a physically meaningful quantity from the logarithmic time delay -- by introducing an IR cutoff, or by considering the derivative of the time delay -- and comment on the bounds implied in each case. Finally, we review a number of additional shockwave backgrounds which might be of use in future applications, including spinning shockwaves, those in higher dimensions or with a cosmological constant, and shockwaves from boosted extended objects.