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On BMS invariance of gravitational scattering

  • Andrew StromingerEmail author
Open Access
Article

Abstract

BMS+ transformations act nontrivially on outgoing gravitational scattering data while preserving intrinsic structure at future null infinity (\( \mathrm{\mathcal{I}} \) +). BMS transformations similarly act on ingoing data at past null infinity (\( \mathrm{\mathcal{I}} \) ). In this paper we apply — within a suitable finite neighborhood of the Minkowski vacuum — results of Christodoulou and Klainerman to link \( \mathrm{\mathcal{I}} \) + to \( \mathrm{\mathcal{I}} \) and thereby identify “diagonal” elements BMS0 of BMS+ × BMS. We argue that BMS0 is a nontrivial infinite-dimensional symmetry of both classical gravitational scattering and the quantum gravity \( \mathcal{S} \)-matrix. It implies the conservation of net accumulated energy flux at every angle on the conformal S 2 at \( \mathrm{\mathcal{I}} \). The associated Ward identity is shown to relate S-matrix elements with and without soft gravitons. Finally, BMS0 is recast as a U(1) Kac-Moody symmetry and an expression for the Kac-Moody current is given in terms of a certain soft graviton operator on the boundary of \( \mathrm{\mathcal{I}} \).

Keywords

Scattering Amplitudes Classical Theories of Gravity Space-Time Symmetries 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Center for the Fundamental Laws of NatureHarvard UniversityCambridgeU.S.A.

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