Abstract
We discuss how scattering amplitudes in 4d Minkowski spacetime which involve multiple soft gravitons realize the algebra of BMS charges on the null boundary. In particular, we show how the commutator of two such charges is realized by the antisymmetrized consecutive soft limit of the double soft amplitude. The commutator is expected to be robust even in the presence of quantum corrections, and the associated Lie algebra has an extension, which breaks the BMS symmetry if the BMS algebra is taken to include the Virasoro algebra of local superrotations. We discuss the implications of this structure for the existence of a 2d CFT dual description for 4d scattering amplitudes.
Highlights
The wavefunction invariant they can lead to physical Ward identities involving the associated Goldstone bosons
We discuss how scattering amplitudes in 4d Minkowski spacetime which involve multiple soft gravitons realize the algebra of BMS charges on the null boundary
The associated Ward identities of the residual symmetries are phrased in terms of relations between the soft limit of an (N + 1)-point function on the one hand and a symmetry transformation acting on an N point function on the other
Summary
The wavefunction invariant (i.e., they are spontaneously broken) they can lead to physical Ward identities involving the associated Goldstone bosons. The full charge Q = QS + QH commutes with the operator O It was recently shown in [6, 7] that Weinberg’s soft graviton theorem for scattering amplitudes [8] is related to the Ward identities of the BMS symmetries [9,10,11] of asymptotically Minkowski spacetimes, with the soft graviton playing the role of the Goldstone boson. It is fair to say, that whether it is possible to have a well-defined holographic theory living on the null boundary, and how such a theory dual to Minkowski space should behave, is still not well understood
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