Gravitational Memory in Higher Dimensions

TL;DR

This work unifies gravitational memory, soft graviton theorems, and asymptotic symmetries in all even spacetime dimensions $d>4$ by showing a universal memory at Coulombic order $r^{3-d}$ and embedding it in an infrared triangle. By developing the general GR framework in $d=2m+2$, deriving residual large diffeomorphisms parameterized by a sphere function, and explicitly constructing memory in $d=6$ (with its Ward identity form and antipodal conservation), the authors extend the 4d IR triangle to higher even dimensions. They then generalize both the memory formula and the corresponding Ward identities to all even $d$, demonstrating that memory, soft theorems, and asymptotic symmetries remain tightly linked through a universal structure. The results illuminate how large diffeomorphisms act as physical asymptotic symmetries and how their associated Goldstone modes govern memory across dimensions, with potential implications for IR behavior in gravitational scattering.

Abstract

It is shown that there is a universal gravitational memory effect measurable by inertial detectors in even spacetime dimensions $d\geq 4$. The effect falls off at large radius $r$ as $r^{3-d}$. Moreover this memory effect sits at one corner of an infrared triangle with the other two corners occupied by Weinberg's soft graviton theorem and infinite-dimensional asymptotic symmetries.