Journal of High Energy Physics · 2014 · 679 citations · 13 references
BMS+ and BMS− transformations act nontrivially on outgoing and ingoing gravitational scattering data at future and past null infinity, respectively, while preserving the intrinsic structure of null infinity. The paper aims to apply Christodoulou and Klainerman’s results within a finite neighborhood of the Minkowski vacuum to link future and past null infinity and identify diagonal BMS0 elements of the BMS+ × BMS− group. This is achieved by leveraging Christodoulou and Klainerman’s analysis of the Einstein equations in a finite region around Minkowski space to relate I⁺ and I⁻. They find that the diagonal BMS0 symmetry is an infinite‑dimensional, nontrivial symmetry of both classical gravitational scattering and the quantum gravity S‑matrix, implying conservation of net energy flux at every angle on the conformal S² at future null infinity, with a Ward identity linking S‑matrix elements with and without soft gravitons, and recasting BMS0 as a U(1) Kac‑Moody symmetry whose current is expressed via a soft graviton operator on the boundary of I⁺.
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 $$ \mathrm{\mathcal{I}} $$ .
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