Strominger, Andrew2016-11-082014Strominger, Andrew. 2014. “On BMS Invariance of Gravitational Scattering.” J. High Energ. Phys. 2014 (7) (July). doi:10.1007/jhep07(2014)152.1029-8479http://nrs.harvard.edu/urn-3:HUL.InstRepos:29374082BMS+ transformations act nontrivially on outgoing gravitational scattering data while preserving intrinsic structure at future null infinity (I +). BMS− transformations similarly act on ingoing data at past null infinity (I −). In this paper we apply - within a suitable finite neighborhood of the Minkowski vacuum - results of Christodoulou and Klainerman to link I + to 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 S-matrix. It implies the conservation of net accumulated energy flux at every angle on the conformal S 2 at 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 I.en-USJournal Article2016-11-0810.1007/JHEP07(2014)152