On memory effects in odd spacetime dimensions

We establish the existence of a new electromagnetic memory effect in all odd spacetime dimensions. This effect is a universal property of electromagnetic fields sourced by charged particles of constant momenta, appears at the Coulombic order and is directly related to the Weinberg soft theorem. We provide a unified derivation of this effect in all higher dimensions by evaluating the Maxwell constraint on a null plane at large, finite distance. We observe that in odd spacetime dimensions, the lightray integral computing the memory effect does not commute with the large-$r$ expansion. Our results necessarily assume that the lightray integral is taken prior to the $r \rightarrow \infty$ limit. The effect vanishes in the opposite order of limits, in agreement with previous results. We compute the Coulombic order electromagnetic memory effect for both massless and massive sources in all higher dimensions, explain its relation to the Fourier transform of the leading soft photon theorem and present a protocol for its measurement in a finite time parametrically larger than the distance of a detector from the sources. We conclude with comments on the generalization to gravity.