Logarithmic soft graviton theorems from superrotation Ward identities

TL;DR

This paper links logarithmic one-loop corrections in soft graviton theorems to superrotation Ward identities, showing they stem from conservation laws at spatial infinity and gravitational tails.

Contribution

It demonstrates that logarithmic soft graviton corrections are encoded in superrotation Ward identities, extending the understanding of asymptotic symmetries in gravitational scattering.

Findings

Logarithmic corrections are derived from superrotation fluxes at null infinity.

Gravitational tails are related to superrotation charges and their conservation.

Massive particles contribute to these corrections via charges at timelike infinity.

Abstract

Soft graviton theorems receive one-loop contributions that are logarithmic in the energy of the soft graviton, and which are closely related to tails of gravitational waveforms. We demonstrate that these logarithmic corrections are encoded in the Ward identity of superrotation symmetries, i.e. they follow from conservation of superrotation charge across spatial infinity $i^0$. Our proof relies on a careful analysis of the radiative phase space admitting such gravitational tails, and the determination of the fluxes through null infinity $\mathscr I$ that act as canonical generators of superrotations on both gravitational and matter fields. All logarithmic terms are derived from the fluxes through correlations of the supertranslation Goldstone mode, provided care is taken in manipulating gravitationally interacting (i.e. dressed) rather than free fields. In cases where massive particles take part in the scattering process, logarithmic corrections also partly arise from the superrotation charge generator at timelike infinity $i^\pm$.