We argue that BMS0 is a nontrivial infinite-dimensional symmetry of both classical gravitational scattering and the quantum gravity S-matrix

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

In this paper we argue that in a finite neighborhood of the Minkowski vacuum classical gravitational scattering is BMS-invariant, and that the perturbative quantum gravity S-matrix — assuming it exists2 — obeys the corresponding relation

We use the results of Christodoulou and Klainerman to show that, in a suitably defined finite neighborhood of the vacuum, i0 is just smooth enough to allow a canonical identification between elements of B+ and B−, and “diagonal’ generators B0 of BMS+×BMS−

Supertranslation invariance of the S matrix in the form implies that, for CK-type configurations which begin and end in the vacuum: The total incoming energy flux integrated along any null generator on I− equals the total outgoing energy flux integrated along the continuation of this null generator on I+

This leads us to suspect the asymptotic symmetry transformations, whose elements by definition act nontrivially, is generated by only one current, which we will take to be the holomorphic one: Pz. While we have not ruled out some other use of the antiholomorphic current Pz, inclusion of the Pzcurrent algebra would appear to be redundant

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